Download If 3x is one factor of , what is the other factor

Name: ________________________
Mr. Art
Date: _____________
Period: ___________
Review # _____
Quadratic Equations
Algebraically
Part I: Linear vs. Quadratic Equation
Graphically
1) Linear Equation: 7th grade
 Degree: _______
 Graph: ________________________
2) Quadratic Equation: 8th grade
Algebraically
Graphically
 Degree: _______
 Graph: _________________________
* When solving quadratic equations we are looking for the zeros, roots
or solutions of the equation. This is where the parabola (graph)
intersects the x-axis.
y = x2 - 3x - 28
Directions: Complete the table below.
Equation
Degree
Type of Equation
3x + 7 = 10
x2 + 6x + 5 = 0
x ( x - 3 ) = 10
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Lesson 6-1: Quadratic Equations = 0 & Lesson 6-2: Quadratic Equations  0
Steps:
1) Standard Form: ax2 + bx + c = 0 (Set equal to zero)
 x2 term must be positive.
 Move all terms to the side where + x2 is.
 If you are given -x2, subtract it over to the
other side of the equation to make it positive.
x 2  7 x  10
2) Factor completely
3) Set each factor equal to zero ("T" it off )
4) Solve each equation for the variable
5) Solution Set (b/c we may have multiple solutions)
6) Optional Check (each solution)
Checks:
Solution #1:
*Step 0: Distribute when you have a
monomial times a binomial or
trinomial.
x 2  3 x
Solution #2:
2 x 2  5  10 x  7
*This step is performed before step 1
if there are parentheses.
xx  2  35
2
Lesson 6-3: Word Problems
Let Statements:
1) When the problems provides variables  No need for Let Statements
2) When you introduce the variable  Let statements
Easy:
The square of a number is 64. Find the number.
Medium:
The square of a positive number is equal to 8 times the number increased by 20. Find the number.
Hard:
Find two positive numbers in the ratio of 2:3 whose product is 150.
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Lesson 6-4: Consecutive Integer Problems
 Consecutive: one after another
Beginning of the problem
End of the problem
Let Statements:
Positive or Negative Integers:
1) Consecutive Integers  x, x + 1, x + 2
1) Positive Integers  reject negative answers
2) Consecutive Even Integers  x, x + 2, x+ 4
2) Negative Integers  reject positive answers
3) Consecutive Odd Integers  x, x + 2, x+ 4
 NOT x, x + 1, x + 3!
Easy Consecutive Integers:
The product of two consecutive integers is 110. Find the integers.
Easy Consecutive Odd Integers:
The product of two consecutive, positive odd integers is 143. Find the integers.
4
Medium Consecutive Odd Integers:
Find two consecutive positive integers such that the square of the first decreased by 25 equals three
times the second.
Hard Consecutive Integers:
Find two consecutive integers such that the sum of their squares is 421.
5
Lesson 6-5: Area Problems
 When using Algebra to solve Geometry problems, remember that dimensions can never be negative!
 Because of this, we always reject negative answers.
1) The length of a rectangle is 6 inches more than its width. The area of the rectangle is 91 square
inches. Find the dimensions of the rectangle.
2) The altitude of a parallelogram measures 5 centimeters less than its base. The area of the
parallelogram is 50 square centimeters. Find the lengths of the base and the altitude.
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Lesson 6-6: Quadratic Proportions
Steps:
1) Parentheses around binomials
2) Cross Multiply
3) Solve
Easy: Solve for x algebraically.
4
x

x 49
Medium:
Which value of x is a solution of
5 x  13

?
x
6
(1)  2
(3)  10
(2)  3
(4)  15
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