Download Quadratic Equations - Review - 2012-2013 - Answers

Name: ________________________
Mr. Art
Date: _____________
Period: ___________
Review # _____
Quadratic Equations
Algebraically
Part I: Linear vs. Quadratic Equation
Graphically
1) Linear Equation: 7th grade
 Degree: __1__
 Graph: ___Line________________
2) Quadratic Equation: 8th grade
Algebraically
Graphically
 Degree: ___2___
 Graph: ____Parabola______________
* 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
1
Linear
x2 + 6x + 5 = 0
2
Quadratic
2
Quadratic
1
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.
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:
*Step 0: Distribute when you have a
monomial times a binomial or
trinomial.
*This step is performed before step 1
if there are parentheses.
x can equal zero, so keep
x = 0 as one of your
solutions.
2 cannot equal zero, so we reject it!
*Remember: a Quadratic should
2
only have at most 2 solutions
anyway.
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.
Faster but more risky method:
Remember:
(+8)(+8) = 64 and (-8)(-8) = 64.
Medium:
10
Hard:
3
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:
Easy Consecutive Odd Integers:
4
Medium Consecutive Odd Integers:
Hard Consecutive Integers:
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.
6
Lesson 6-6: Quadratic Proportions
Steps:
1) Parentheses around binomials
2) Cross Multiply
3) Solve
Easy:
Medium:
7