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Algebra II / Trigonometry
Unit 3
Quadratics
Unit 3: Quadratics
Date
Topic
Day 1 – Solving Quadratic Equations by Factoring
Classwork Homework
Pages
Pages
3-4
5-8
Day 2 – Solving Quadratic Inequalities by Factoring
9-10
11-13
Day 3 – Solving Rational Equations / Check Roots
14-15
16-18
Day 4 – Solving Rational Inequalities (graphically only)
19-21
22-24
Day 5 – Completing the Square to find the Roots (1)
25-27
28-30
Day 6 – Completing the Square to find the Roots (2)
31-33
34-35
Day 7 – QUIZ / Using the Quadratic Formula to find the Roots of
a Polynomial
(Note: Quiz will include Days 1-5 only)
Day 8 – Finding the Product and Sum of the Roots, and Finding
the Equation given the Roots
Day 9 – Given One Root, Find the Second Root of an Equation
36-37
38-39
40-41
42-43
44-45
46-48
Day 10 – Solving Higher Degree Polynomial Equations Using
Factor By Grouping
Day 11 – Solving Higher Degree Polynomial Equations
49-51
52-53
54-55
56-57
Day 12 – Solving Higher Degree Polynomial Equations /
Graphically
Day 13 – Systems of equations / inequalities algebraically
58-59
60
61-63
64-66
Day 14 – Systems of equations / inequalities graphically
** Don’t forget your index cards tomorrow **
Day 15 – Review
67-69
70-72
73-75
Study!
Day 16 – TEST
Page 2
Day 1 – Solving Quadratic Equations by Factoring
Steps to Solving Quadratic Equations by Factoring:
1.) Simplify the equation. (For example, distribute)
2.) Set the equation equal to zero. (In standard form: ax 2  bx  c  0 , where a  0 )
3.) Factor.
4.) Set each factor to zero.
5.) Solve each resulting equation for x.
Directions: Solve each quadratic equation.
2.) 9  x6  x 
1.) x 2  4  3x
3.) 3x 2  4 x  1  0
Page 3
4.) 3x 2  27  0
Practice Problems
Directions: Solve each quadratic equation.
5.) 10 x  21  x 2
6.) 3x 2  5 x  36  2 x
7.) 2 xx  1  12
8.) 3x 2  4 x  4
Page 4
Day 1 – Solving Quadratic Equations by Factoring
HOMEWORK
**Complete any Practice Problems from class work that have not been completed**
Directions: Solve each quadratic equation.
1.) x 2  6 x  5  0
2.) x 2  10 x  24  0
3.) x( x  7)  2  28
Page 5
4.) 4  x( x  3)  0
5.) 2 x 2  6 x  108
6.) 7  x8  x 
7.) 4 x 2  81  0
8.) 4 x 2  x  5
Page 6
9.) 18  7 x  x 2  0
10.) 2 x 2  50  0
11.) The width of a rectangle is 12 feet less than the length. The area of the rectangle is 28 square feet.
Find the dimensions of the rectangle.
Review
12.) Express the sum is simplest radical form:
2  18   4  50

Page 7
 

13.) Express in simplest form: 31  2 x    x  2 
2
14.) Write
3 5
3 5
Page 8
with a rational denominator in simplest radical form.
Day 2 – Solving Quadratic Inequalities by Factoring
Do Now: (Questions 1 & 2)
1.) The solution set of x 2  2 x  8  0 is
(1) {2, 4}
(3) {2, -4}
(2) {-2, 4}
(4) {-2, -4}
2.) Find the roots of the given equation:
2 x 2  x  12  x
Steps to Solving Quadratic Inequalities by Factoring:
1.)
2.)
3.)
4.)
5.)
6.)
Simplify the inequality. (For example, distribute)
Move each term to one side of the inequality with zero on the other side.(Remember you want a  0 )
Factor.
Set each factor to zero.
Solve each resulting equation for x.
Graph or write the solution set.
a.) If the inequality sign makes a “C” for connect the solution set is all connected together.
b.) If the inequality sign does NOT make a “C” the solution set is NOT connected and the word
“OR” is used to write the solution.
Directions: Write the solution set and graph each quadratic inequality.
3.) x 2  2 x  15  0
4.) x 2  3x  4
Page 9
5.) 3 x 2  17 x  6
6.)  2 x 2  2 x  24  0
Practice Problems
Directions: Write the solution set and graph each quadratic inequality.
9.) x 2  2 x  0
10.) 4 x 2  16 x  12  0
Page 10
Day 2 – Solving Quadratic Inequalities by Factoring
HOMEWORK
**Complete any Practice Problems from class work that have not been completed**
Directions: Write the solution set and graph each quadratic inequality.
1.) x 2  x  56  0
2.) x 2  3x  2 x  4
3.)
2x 2  7x  3  0
Page 11
4.)
x 2  4 x  12
5.)
x 2  4x  x
6.)
4x 2  9
Review
49
a
Simplify:
14
a9
a
a
7.)
Page 12
8.) Perform the indicated operation and simplify:
2 x  7   2 1
2 x  5x  7
9.) The length of Bill’s rectangular garden is 2 yards more than four times the width. The area of the
garden is 30 square yards. What are the dimensions of the garden?
Page 13
Day 3 – Solving Rational Equations / Check Roots
Do Now: (Questions 1 & 2)
1.) Solve for x: x 2  6 x  5  0
(1)  x  5 or  x  1 (3)
(2)
 5  x  1
(4)
 x  5 or  x  1
1  x  5
2.) What is the graph of the solution set of
x2  2x  3  0 ?
(1)
-1
3
(2)
-1
3
(3)
-1
3
-1
3
(4)
Steps to Solving Rational Equations:
1. Multiple each term on both sides of the equation by the least common denominator.
2. Cancel out the denominators.
3. Solve the resulting equation.
4. Check to make sure that the solutions do not make the original equation undefined.
Directions: Solve each equation.
a2 a2
2 4 5

3.)
4.)  
a
2a
3 x 6
Page 14
5.)
10 3
 1
x2 x
6.)
2
20
 2
1
x  5 x  25
8.)
5
3
21

 2
a  3 a  4 a  7a  12
Practice Problems
Directions: Solve each equation.
3 5 1

7.) 
a 2a 2
Page 15
Day 3 – Solving Rational Equations / Check Roots
HOMEWORK
**Complete any Practice Problems from class work that have not been completed**
Directions: Solve each equation.
4 9  4x x
b
30


1.) 
2.) 4 
x
3x
3
b5 b5
3.) 2 
4
6x  4
 2
x2 x 4
Page 16
4.)
y
2
y 5

 2
y  4 y 1 y  3y  4
5.)
x 1 2
4
  2
x  2 x x  2x
6.)
2b
1
10

 2
5  b 5  b b  25
Review
7.) Express in simplest form:
b
3b

2b  1 8b  4
Page 17
2
1
a
8.) Simplify:
4
a
a
3
10a 2 b
9.) Simplify:

9
5ab 2
Page 18
10.) Solve for b: 8  2b  3  9
Day 4 – Solving Rational Inequalities
Do Now: (Question 1)
1.) Solve for x:
4x
12
 2
x 3
x 3
Steps to Solving Rational Inequalities:
1. Move all terms onto the left side of the inequality using either addition or subtraction.
2. Find a common denominator, and combine all fractions into a single term.
3. Find the “critical values” by setting the numerator = 0 and solve, and set the denominator = 0 and
solve. This will give you the x-intercepts or the asymptotes. (Note: If the denominator is an integer,
then there is no critical value for the denominator.)
4. Graph the inequality as an equation in y=. (Wrap the numerator, wrap the denominator for each
term.)
5. Write your solution. If the original inequality is >0, then look for the solution where the graph is
above the x-axis. If the original inequality is <0, then look for the solution where the graph is below
the x-axis.
Directions: Solve each inequality.
x 1 x 3
  
2.)
4 8 3 8
Page 19
3.) 2 
4.)
3 5

a a
x 3 x  2

5
10
Page 20
5.)
a 1
a
 11 
4
6
Page 21
Day 4 – Solving Rational Inequalities
HOMEWORK
Directions: Solve each inequality.
3b  4 4b  3

1.)
8
4
2.)
7 2 3
 
2 x 2
Page 22
3.) 3 
4.)
2
5
a 1
4x
2
2
x4
x4
Page 23
Review
7.) Solve for x:
x5
1
1  2
2
x  2x
x  2x
2a 2  ab  3b 2 4a  4b
9.) Simplify:

a 2  36b 2
8a  48b
Page 24
8.) What is the solution set for the equation:
3x  1  x  5
10.) Express with a rational denominator in simplest
3 2
radical form:
3 2
Day 5 – Completing the Square to find the Roots (1)
Do Now: (Questions 1 & 3)
1.) Solve the inequality:
5

(1)   3  x   
3

(2)
3.)
5

  x  3
3

3x  5
0
x3
2.) Solve for x:
5

(3)  x  3or  x   
3


(4)  x 

2x
1
1 
x2
x2
(1) x  1or x  2
(3) 1  x  2
(2) x  1or x  2
(4)  2  x  1
5
or  x  3
3
ax 2  bx  c  0
Standard form of a quadratic equation:
Find a, b, c given the quadratic equation 3x 2  8 x  11 = 0.
Steps for Completing the Square (when a = 1)
1.)
2.)
3.)
Rearrange the equation to be in the form ax 2  bx  c
Rewrite the equation with a blank space at the end of each side to insert the result from step 3.
Ex) ax2 + bx + _______ = c + _____
Divide b by 2, and then square the result.
2
b
Fill in   (the number from step #3) on both sides of the equation.
2
5.) Factor the left side. (Write as a perfect square in factored form.)
6.) Take the square root of each side of the equation. (Don’t forget both positive and negative.)
7.) Solve for x.
8.) Simplify (if possible).
Directions: Solve for x, in simplest radical form, if possible.
4.) x 2  6 x  8  0
4.)
Page 25
5.) x 2  8 x  4
6.) Solve for the positive root, to the nearest tenth.
23
 x  10
x
Page 26
Practice Problems
Directions: Solve for x, in simplest radical form, if possible.
7.) x 2  9  8 x
8.) x 2  2 x  24  0
Page 27
Day 5 – Completing the Square to find the Roots (1)
HOMEWORK
**Complete any Practice Problems from class work that have not been completed**
Directions: Solve for x, in simplest radical form, if possible.
x 2  12 x  12  0
1.)
2.) x 2  12 x  5  0
3.)
x 2  2  4 x
Page 28
4.)
x2  2x  2  0
5.)
x2  2 x  5  0
6.)
x2  6x  2  0
7.)
x2  8x  4  0
8.)
x 2  10 x  6  0
Page 29
Review
5
9.) Simplify:
Page 30
45
a2
3
1
a
10.)
Solve for x:
x x
 7
5 10
Day 6 – Completing the Square to find the Roots (2)
Do Now: (Questions 1 & 2)
1.) What number must be added to both sides of the
equation x 2  5 x  3 to solve it by completing the
square?
(1) 225
(2) 25
2.) Solve x 2  6 x  2  0 by completing the
square, expressing the result in simplest form.
(3) 6.25
(4) 5
Steps for Completing the Square when a  1
1.) Rearrange the equation to be in the form ax 2  bx  c
*NOTE: If a  1 , divide each term of the equation by a to make a  1 .
2.) Rewrite the equation with a blank space at the end of each side to insert the result from step 3.
Ex) ax2 + bx + _______ = c + _____
3.) Divide b by 2, and then square the result.
2
b
4.) Fill in   (the number from step #2) on both sides of the equation.
2
5.) Factor the left side. (Write as a perfect square in factored form.)
6.) Take the square root of each side of the equation. (Don’t forget both positive and negative.)
7.) Solve for x.
8.) Simplify (if possible)
Directions: Solve for x, in simplest radical form, if possible.
3.) 2 x 2  12 x  6
Page 31
4.) 3x 2  6 x  1  0
5.) 2 x 2  x  1  0
Page 32
6.)
1 2 3
3
x  x 0
4
4
2
Practice Problems
7.) 2 x 2  6 x  3  0
Page 33
Day 6 – Completing the Square to find the Roots (2)
HOMEWORK
**Complete any Practice Problems from class work that have not been completed**
Directions: Solve for x, in simplest radical form, if possible.
1.) 2 x 2  8 x  4
2.) 3x 2  6 x  2  0
3.) 4 x 2  20 x  9  0
Page 34
4.)
1 2
x  x3  0
2
Review
5.) Perform the indicated operation. Simplify your answer to lowest terms.
y 2  y  12 y 2  11y  30

y 2  y  20 y 3  9 y 2  18 y
6.) Rationalize the denominator in simplest form:
Page 35
1 2 5
5 5
Day 7 – Using the Quadratic Formula to find the Roots of a Polynomial
Do Now: QUIZ
Steps for Solving using the Quadratic Formula
1.)
Rearrange the equation to be in the form ax 2  bx  c  0 .
b  b2  4ac
2.) Substitute the appropriate values for a, b, and c into the formula: x 
2a
3.) Simplify the radical expression as much as possible, or round the answer as instructed.
Directions: Use the quadratic formula to find the roots of each equation, in simplest form.
1.) x 2  1  4 x
2.) 2 x  6 
3
x
Page 36
3.) Use the quadratic formula to find the roots of 10  2 x  6  x to the nearest tenth.
Page 37
Day 7 – Using the Quadratic Formula to find the Roots of a Polynomial
HOMEWORK
Directions: Use the quadratic formula to find the roots, in simplest radical form if possible.
1.) 2 x 2  8 x  4
2.) 3x 2  6 x  2  0
3.) 4 x 2  20 x  9  0
Page 38
4.)
1 2
x  x3  0
2
Review
5.) Perform the indicated operation. Simplify your answer to lowest terms.
a 2  3a  10 5a  a 2

5a
15
6.) Rationalize the denominator in simplest form:
Page 39
4
x 8
Day 8 – Finding the Product and Sum of the Roots, and Finding the Equation given the Roots
Do Now: (Question 1)
1.) Solve this equation for x. An algebraic solution is required. Express the answer in simplest radical
form: x 2   x  4
Steps for Finding the Sum and Product of the Roots
Rearrange the equation to be in the standard form ax 2  bx  c  0
b
c
Sum =
, Product =
a
a
Directions: For each equation, solve for the sum and product of the roots.
2.) x 2  6 x  8  0
3.) x 2  8 x  11  0
4.) 2 x 2  x  24  0
5.) 3x 2  9  8 x
Steps for Writing the Quadratic Equation When Given the Roots of the Equation
1.) Solve for the sum and the product of the roots
2.) Fill the sum and product of the roots into the standard form of the equation:
x 2  (sum) x  ( product )  0
3.) If necessary, multiply all terms by the greatest common denominator.
Page 40
Directions: Write a quadratic equation with integer coefficients for each pair of roots.
6.) 4, 7
7.) –3, 3
8.)
1 7
,
2 2
Page 41
9.) Write a quadratic equation with integer
coefficients when given one root : 3  2
Day 8 – Finding the Product and Sum of the Roots, and Finding the Equation given the Roots
HOMEWORK
Directions: Without solving each equation, find the sum and product of the roots.
x2  x  1  0
1.)
2.) 2 x 2  3x  2  0
3.)
 x 2  3x  1  0
4.)
8 x  12  x 2
Directions: Write a quadratic equation with integer coefficients for each pair of roots.
5.) 2, 5
3 3
,
6.)
4 8
Page 42
Directions: Given one of the roots, write a quadratic equation with integer coefficients.
7.) 2  3
8.) 5  3
Review
9.) Write
3 5
as an equivalent fraction with a rational denominator.
3 5
2
m and list all values of m for which the fraction is undefined.
10.) Simplify the rational expression
1
1 2
m
2
Page 43
Day 9 – Given One Root, Find the Second Root of an Equation
Do Now: (Questions 1 & 2)
1.) For which equation does the sum of the roots
3
equal
and the product of the roots equal –2?
4
(1) 4 x 2  8 x  3  0
(2) 4 x 2  8 x  3  0
(3) 4 x 2  3 x  8  0
(4) 4 x 2  3x  2  0
2.) Find the values of b and c in the following
equation if the roots of the equation are 6, 1 :
x 2  bx  c  0
Steps for Finding the Second Root When One is Given
Method 1:
1.)
2.)
Use the equation given to determine either the sum or product of the roots.
Write an equation to find the second root.
Ex) If first root = 5 and sum = 8, then 5 + x = 8
Method 2:
1.)
2.)
Plug the first root into the equation for x to solve for the missing variable.
Solve the equation using one of your three methods (factoring, completing the square, or the quadratic
formula) to find the second root.
Directions: One of the roots is given. Find the other root.
3.) The equation x 2  8 x  c  0 has one root equal to –3. Find the other root.
Page 44
4.)
The equation x 2  bx  8  0 has one root equal to 4. Find the other root.
Practice Problems
5.) The equation x 2  3x  k  0 has one root equal
to 5. Find the other root.
Page 45
6.) The equation 2 x 2  5 x  k  0 has one root equal
to -3. Find the other root.
Day 9 – Given One Root, Find the Second Root of an Equation
HOMEWORK
**Complete any Practice Problems from class work that have not been completed**
Directions: One of the roots is given. Find the other root.
1.) x 2  15 x  c  0 , one root = –5
2.) The equation m2  4m  n  0 has one root
equal to 3. Find the other root.
3.) 3x 2  10 x  c  0 , one root = -4
Page 46
4.) x 2  kx  15  0 , one root = 3
Review
5.) Solve for x:
2x  1 2x  2

2
3
x
ab
b
6.) Simplify:
b
1
a
Page 47
7.) For what values of x is the fraction undefined?
2x  4
2
x  6x  8
8.) Find the solution set and graph : 2 x 2  5 x  7
Page 48
9.) Solve for x: x  3  29  5 x
Day 10 – Solving Higher Degree Polynomial Equations Using Factor by Grouping
Do Now: (Questions 1 & 2)
2.) If one root of a quadratic equation is 3 and the
1.) If one root of the equation 2 x 2  10 x  k  0 is
product of the roots is 15, what is the value of b if the
2 , what is the other root?
equation is in the form ax 2  bx  c  0 and a  1 .
(1) 8
(3) 3
(1) 5
(3) 8
(2) 3
(4) 5
(2) -5
(4) -8
Steps for Solving Using Factor by Grouping
Consider the expression: 2 x 3  7 x 2  8 x  28
1.) Move all terms to one side on the equation: 2 x 3  7 x 2  8 x  28  0 (Keep the leading coefficient
positive)
2.) Examine this example as two sets of binomials: 2 x 3  7 x 2
and  8x  28 . (When viewed
independently, each binomial contains a different greatest common factor.
3.) Rewrite each binomial expression in factored form: x 2 2 x  7 + 42x  7 . (Notice that the two
binomials now contain a common factor 2x  7 in the parentheses.
4.) The factor 2x  7 becomes the new GCF and the “leftovers” go in the other set of parentheses.
5.)
6.)


Therefore in factored form 2 x  7 x 2  4 = 0.
Set each factor equal to zero and solve. (T-OFF)
(Note: When x2 equals a number, you need the positive and negative square root.)
Page 49
Directions: Solve each equation by grouping.
3.) 3x 3  5 x 2  12 x  20
5.) 8 x 3  6 x 2  4 x  3  0
Page 50
4.) 25 x 3  75 x 2  x  3
Practice Problems
Directions: Solve each equation by grouping.
6.) 2 x 3  7 x 2  8 x  28
Page 51
7.) 3x 3   x 2  3x  1
Day 10 – Solving Higher Degree Polynomial Equations Using Factor by Grouping
HOMEWORK
**Complete any Practice Problems from class work that have not been completed**
Directions: Solve each equation by grouping.
1.) x 3  2 x 2  9 x  18
2.) 3x 3  2 x 2  12 x  8
3.) 3x 3  4 x 2  6 x  8  0
Page 52
4.) 6 x 3  4 x 2  9 x  6
Review
5.) Express in simplest form: 31  2 x   x  2 .
6.) Find the solution set: x 2  2 x  8  0
1
2
7.) Express in simplest form:
3
2
4
8.) Find the product of 2  18  4  50 in
simplest radical form.
2
1
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


Day 11 – Solving Higher Degree Polynomial Equations
Do Now: (Questions 1 & 2)
1.) Factor the following: x 3  5 x 2  4 x  20
(1) x 2  4 x  5
(3) x 2  4 x  5
(2) x 2  4 x  5
(4) not factorable






2.) Factor the following: uv  4u  5v  20
(1) v  4u  5
(3) 5uv  4
(2) v  4v  5
(4) v  4u  5
Steps for Solving Higher Degree Equations
1.) Use all of your factoring skills: GCF, DOTS, Trinomials, and Grouping.
2.) Set each factor equal to zero. (T-OFF)
3.) Solve
Directions: Use your factoring skills to find all solutions for x.
3.) 3x 3  x 2  10 x
4.) 6 x 4  21x 3  18 x 2  0
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5.) x 5  16 x  17 x 3
6.) 4 x 2  5  
Practice Problems
Directions: Use your factoring skills to find all solutions for x.
6.) 2 x 3  162 x  0
7.) 5 x 3  5 x
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1
x2
Day 11 – Solving Higher Degree Polynomial Equations
HOMEWORK
**Complete any Practice Problems from class work that have not been completed**
Directions: Solve each equation.
1.) x3  5 x 2  4 x  0
2.) x 4  10 x 2  9  0
3.) 4 x 4  52 x 2  144  0
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4.) 5 x 3  125 x  0
Review
1
x
5.) Write in simplest form:
x 1
x
7.) For what value(s) of x does
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x  3 2x 1

?
2
3
6.) Find the solution set of the equation
x2 – 2x – 8 < 0 and graph on a number line.
8.) Solve 2 x 2  3x  2  0 by completing the square.
Day 12 – Solving Higher Degree Polynomial Equations / Graphically
Do Now: (Questions 1 & 2)
1.) What are the solutions of this equation
x 4  10 x 2  9  0 ?
(1) {-1 , 1}
(3) {3, -3, 1}
(2) {-1, 1, 3}
(4) {-1, 1, -3, 3}
2.) What are the solutions of this equation:
6 x 3  6 x  5x 2 ?
3 2
 3 2
(1)  , 
(3)  , 
2 3
 2 3
3 2

 3 2
(2) 0, , 
(4) 0, , 
2 3

 2 3
Steps for Solving Higher Degree Equations by Graphing
1.)
2.)
3.)
4.)
5.)
6.)
Move all terms to the same side of the equation.
Enter the equation into y = on your calculator.
Graph the equation.
To identify the real roots use the calculator’s 2nd TRACE function.
Choose option number 2. (zero)
You must identify the left bound of the zero, so move your cursor to the left of the first zero and
press ENTER.
7.) Move your cursor to the right of the zero you wish to identify. Then press ENTER.
8.) To guess, press ENTER again and you will see the solution. (x = ?)
9.) Repeat the steps for all zeros.
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Directions: Solve each equation using your graphing calculator.
3.) 3x 4  5 x 3  5 x 2  5 x  2  0
4.) 3x 4  7 x 3  18 x 2  28 x  24  0
5.) 2 x 4  3x 3  28 x 2  12 x  80  0
6.) x 4  6 x 3  7 x 2  96 x  144  0
Practice Problems
Directions: Solve each equation using your graphing calculator.
7.) x 4  x 3  3x 2  x  2  0
8.) 3x 5  2 x 4  35 x 3  18 x 2  72 x  0
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Day 12 – Solving Higher Degree Polynomial Equations / Graphically
HOMEWORK
**Complete any Practice Problems from class work that have not been completed**
Directions: Solve each equation using your graphing calculator.
1.) 8 x 4  12 x 3  22 x 2  3x  5  0
2.) 8 x 4  18 x 3  3x 2  17 x  6  0
3.) 15 x 3  2 x 2  48 x  32  0
Review
4.) Find the roots by completing the square:
3x 2  6 x  6  0
5.) Find the roots by using the quadratic formula, in
simplest radical form: 5 x 2  2 x  1
6.) Find the three binomial factors of
x 3  x 2  4 x  4 by factoring.
7.) Write the quadratic equation given the roots -3
and 5.
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Day 13 – Solving Systems of Equations Algebraically
Do Now: (Questions 1 & 2)
1.) The zero(s) of the following graph are
(1)
(2)
(3)
(4)
2.) Find the zeros of 3x 3  12 x 2  x  4  0
x=0
x = 0 and x = 2
y=0
y = 0 and y = 2
Steps for Solving Systems of Equations Algebraically
Method 1
1.
2.
3.
4.
Solve each equation for y in terms of x.
Set the equations equal to each other.
Solve for x.
Plug the value(s) of x into one of the equations and solve for y.
Method 2
1.
2.
3.
4.
Solve one equation for y
Replace the y with its equivalent in the second equation.
Solve for x.
Plug the value(s) of x into each equation and solve for y.
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Directions: Solve each of the following system of equations algebraically.
y  x2  2x  8
2x 2  x  y  1  0
3.)
4.)
y 8  x
x y7 0
Page 62
Practice Problems
Directions: Solve each of the following system of equations algebraically.
y  13  x
y  x2 1
5.)
6
.)
y  3  x 2  6x
2 x  3  y  3x 2
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Day 13 – Solving Systems of Equations Algebraically
HOMEWORK
**Complete any Practice Problems from class work that have not been completed**
Directions: Solve each of the following system of equations algebraically.
yx2
2 x 2  y  10
1.)
2.)
y  x 2  2x  4
y  2 x 2  3x  12
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3.)
y  2x 2  4x  7
y  4x  x 2  4
Review
4.) Find the solution set of x  2  5 .
Page 65
5.) Express in simplest radical form the sum of
75  27
6.) Factor completely: 2 x 3  2 x 2  2 x  2
Page 66
2
a
7.) Simplify:
1
1 2
a
2
Day 14 – Solving Systems of Equations / Inequalities Graphically
Do Now: (Questions 1)
1.) Solve the following system of equations algebraically:
y  2x 2  6x  5
y  x2
Steps to Solving Quadratic Inequalities in Two Variables
1.) Solve for y in terms of x. (Solve for y)
2.) Graph the quadratic function. (Solid line for equal and dotted line for strictly greater than or less
than.)
3.) Shade the appropriate region by using a test point (or your calculator).
Directions: Graph the given inequality, and label the solution set with S.
2.) y  3  x 2  4 x
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3.) y  2x  2  3
2
4.) Solve the system by graphing and determine the common solution point(s).
y  x 2  2x 1
y  x3
Page 68
Practice Problems
Directions: Graph the given inequality, and label the solution set with S.
5.) y  4 x  x 2
Page 69
Day 14 – Solving Systems of Equations / Inequalities Graphically
HOMEWORK
**Complete any Practice Problems from class work that have not been completed**
Directions: Graph the given inequality, and label the solution set with S.
1.) x 2  4  y
2.) x 2  2 x  3  y
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3.) Solve the system by graphing and determine the common solution point(s).
y  2x2  2x  3
yx3
Review
4.) Rationalize the denominator:
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3
5 2
5.) Express in simplest form:
24  150
6.) Find the roots by completing the square:
x
5

12 2 x  7
7.) Solve for all values of x: x 3  2 x 2  16 x  32  0
Page 72
1.) Solve for all roots by completing the square:
3x 2  6 x  6  0
Day 15 – Review
2.) Solve for all roots using the quadratic formula in
simplest radical form:
5x2  2 x  1
3.) Without solving the equation, find the sum and
product of the roots: 8 x 2  9  6 x
4.) Write a quadratic equation with integer
coefficients when one root is 4  2 .
Page 73
5.) Find all the zeros of the given equation:
x 4  50 x 2  49
6.) Find the common solution algebraically, in
simplest radical form.
y  x2  4x  4
y  4x  6
7.) a.) Graph y  2 x 2  x  3
b.) Is the point (0, 0) a solution to the inequality?
Page 74
8.) If x 2  12 x  k  28 and one root is 2, find the
other root and the value of k.
9.) Find the solution set and graph the solution on a
number line: x 2  x  6  0
11.) Solve:
x
3
4
 
x  2 x x x  2 
Page 75
10.) Solve for all values of x:
4 x 3  8 x 2  25 x  50  0
12.) Solve:
4x
2
2
x4
x4