Unit 5 (Quadratic Equations) Test Review

State the Solutions of The Factored Equation

100

(x+3)(x-7)=0

x=-3 or x=7

200

(x+4)(x+18)=0

x=-4 or x=-18

300

(n-1)(3n+5)=0

n=1 or n=-5/3

400

(2x-7)(3x+9)=0

x=7/2 or x=-3

500

a(a-5)=0

a=0 or a=5

Solving by Factoring (B and C terms both positive)

100

x²+7x+12=0

(x + 3)(x+4) = 0

x=-4 or x=-3

200

x²+8x+12=0

(x+2)(x+6)=0

x=-2 or x=-6

300

x²+11x+10=0

(x+1)(x+10)=0

x=-1 or x=-10

400

x²+10x+24=0

(x+6)(x+4)=0

x=-6 or x=-4

500

x²+10x+25=0

(x+5)(x+5)=0 or (x+5)²=0

x=-5

Solving by Factoring (B and/or C terms could be negative)

100

x²+4x-5=0

(x+5)(x-1)=0

x=-5 or x=1

200

x² - 3x - 10 = 0

(x-5)(x+2)=0

x=5 or x=-2

300

v²-7v+6=0

(v-1)(v-6)=0

v=1 or v=6

400

m²+2m-3=0

x=1 or x=-3

500

r²-10r+24=0

(r-6)(r-4)=0

r=6 or r=4

Checking Solutions

100

Is 2 a solution to the following quadratic equation:

(x - 2)(x + 5) = 0

Yes, 2 is a solution to the quadratic equation.

200

Is 4 a solution to the following quadratic equation:

p²-9p+20=0

Yes, 4 is a solution to the quadratic equation.

300

Are 3 and -7 solutions to the following quadratic equation:

(x + 3)(x - 7) = 0

No, 3 and -7 are not solutions to the quadratic equation.

400

Is 3 a solution to the following quadratic equation:

x²+2x-15=0

Yes, 3 is a solution to the quadratic equation.

500

Are -4 and 7 solutions to the following quadratic equation:

w²+3w-28=0

No, -4 and 7 are not solutions to the quadratic equation.

Free Response

100

State an example of a quadratic equation. 

Since you cannot type exponents in the live lesson room chat use the carrot key (^) to denote exponents.

There are infinite answers.  

Answers should have a variable raised to the second power and no variables raised to a higher power.

200

What is the standard form of quadratic equations?

ax² + bx + c = 0

300

What does the zero product property state?

It states if the product of two factors is 0, then one of the factors must be equal to 0. 

For example: If xy=0 then x or y must equal 0

400

What does it mean for a number to be part of the solution set of a quadratic equation?

For example: If -1 is a solution to the quadratic equation x² + 2x + 1 = 0 what does that actually mean?

It means the number will satisfy the equation (make it true) if we plug the number in for the variable.

For this specific example it would mean if we plug -1 into the equation it will make a true statement.

500

What is the difference between a quadratic equation and a linear equation?

A quadratic equation is of degree 2 (highest power of the variable in the equation is 2) whereas linear equations are of degree 1 (highest power of the variable in the equation is 1).