Quadratic Test Review

Quadratic Test Review

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This is an excellent review tool.

Quadratic Unit Test Concepts

• Vertex and Axis of Symmetry

• Real World quadratic functions

• Quadratic vertex form

• Quadratic standard form

• Quadratic factored form

• Factoring trinomials

• Difference of Two Squares

• Factoring 4 terms by grouping

Multiple Choice

Factor the GCF:

3x³ + 9x² - 15x

• x(3x² + 9x - 15)

• 3x(x² + 3x - 5)

• 3x(x² - 9x + 15)

• x(3x² -9x + 15)

Multiple Choice

Factor into two binomials: x² + 7x - 30

• (x + 10)(x - 7)

• (x - 10)(x + 3)

• (x + 10)(x + 3)

• (x + 10)(x - 3)

Examples of Difference of Two Squares

Multiple Choice

Difference of Two Squares

Factor into two binomials: 4y² – 9.

• (2y + 3)(2y – 3)

• (4y+1)(4y-9)

• (2y + 3)(2y + 3)

• (2y – 3)(2y – 3)

Quadratic Vocabulary

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Multiple Choice

A parabola has a vertex at (-3,2). Where is the axis of symmetry?

• y = -2

• x = 3

• x = -3

• y = 2

Multiple Choice

What is the vertex for the following quadratic?

The quadratic is given to you in vertex form.

y = 3(x - 5)² + 7

• (3, -5)

• (5, 7)

• (7, -5)

• (-5, 7)

​Solving a quadratic using factoring.

Multiple Choice

Solve by factoring

x² + 13x + 12 = 0

• x = -12, -1

• x = 12, 1

• x = 13, 1

• x = -13, -1

Multiple Choice

Solve by factoring: x² - 9x + 20 = 0

• x = -4 and x = -5

• x = 20 and x = -9

• x = 4 and x = 5

• x = -4 and x = 5

Multiple Choice

What is the range of this function?

• All real numbers.

• All real numbers greater than or equal to 0.

• All real numbers greater than or equal to -2.

• All real numbers greater than or equal to 2.

Multiple Choice

The graph below describes a ball that was kicked. Which of the following is a true statement describing the graph?

• The ball was kicked from 500 centimeters from the ground and it traveled for 4 seconds.

• The ball was kicked from the ground and it was in the air for 4 seconds.

• The ball had a maximum height of 2000 centimeters and it was in the air for a total of 2 seconds.

• The ball had a maximum height of 1000 centimeters and it was in the air for 4 seconds.

The vertex

in the given graph

is the only zero of

the quadratic.

The vertex is on the

x-axis.

There are 3 ways to write a quadratic function.

Multiple Choice

Which function below is the quadratic vertex form?

• $$y=\left(x+4\right)\left(x+6\right)\$$

• $$y=\left(x+5\right)^2-1$$

• $$y=x^2+10x+24$$

Multiple Choice

Which function below is the quadratic standard form?

• $$y=\left(x+4\right)\left(x+6\right)\$$

• $$y=\left(x+5\right)^2-1$$

• $$y=x^2+10x+24$$

Multiple Choice

Which function below is the quadratic factored form?

• $$y=\left(x+4\right)\left(x+6\right)\$$

• $$y=\left(x+5\right)^2-1$$

• $$y=x^2+10x+24$$

Multiple Choice

Suzie solves the equation below:

x² + 4x - 12 = 0

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

by setting x -2 = 0 and x + 6 = 0.

Her solutions are x = 2 and x = -6.

Is Suzie correct? Why or why not?

• Yes, she factored correctly and then used the zero product property

• Yes, she factored correctly and then square rooted.

• No, she did factor correctly, but she can't use the zero product property as shown.

• No, she didn't factor correctly so the rest of her work is wrong.

Multiple Choice

Find the zeros.

• x = {0 and 4}

• x = {-4 and 0}

• x = 0

• x = -4

Multiple Choice

Mrs. Altman's 7th grade science class built and launched rockets. The graph below shows the height, in feet, over time, in seconds, of a student's rocket. Use the graph to answer the questions below. How long did it take the rocket to reach its maximum height?

• 1 second

• 5 seconds

• 7 seconds

• 11 seconds

Multiple Choice

A quadratic function has zeros -7 and 9.

What are the linear factors of the function?

• (x+7) (x-9)

• (x-7) (x+9)

• (x+7)(x+9)

• (x-7)(x-9)

Multiple Choice

An object in launched directly upward at 64 feet per second (ft/s) from a platform 80 feet high. Its height is represented by the equation

s(t) = –16t² + 64t + 80

What will be the object's maximum height?

• 2 ft

• 80 ft

• 144 ft

• 64 ft

Multiple Choice

You jump off a 24 foot high cliff and your fall is modeled by the function:

h(t) = -16t² + 8t + 24

How long would it take you to hit the water?

• 8 seconds

• 1 second

• 1.5 seconds

• 1/4 second

Multiple Choice

A diver is standing on a platform above the pool. He jumps form the platform with an initial upward velocity of 8 ft/s. Use the formula: h(t) = −16 t² + 8t + 24

How high is the platform?

• .25 ft

• 24 ft

• 25 ft

• 8 ft

Multiple Choice

Factor:
x² + 5x - 24

• (x - 8)(x + 3)

• (x + 8)(x - 3)

• (x + 6)(x - 4)

• (x + 12)(x - 2)

Multiple Choice

Difference of Two Squares: 9x² - 25

• ( 3x + 5 ) (3x - 5 )

• ( 3x - 5 ) (3x - 5 )

• ( 3x + 5 ) (3x + 5 )

• Unfactorable

Multiple Choice

Factor by grouping: $$20p^3-25p^2+4p-5$$  

• $$\left(5p^2-1\right)\left(4p-5\right)$$  

• $$\left(5p^2+1\right)\left(4p+5\right)$$  

• $$\left(5p^2+1\right)\left(4p-5\right)$$  

• $$\left(5p^2-1\right)\left(4p+5\right)$$  

Multiple Choice

Factor by grouping:

$$4p^3+8p^2+3p+6$$  

• $$\left(2p^2+3\right)\left(p+2\right)$$  

• $$\left(2p^2+6\right)\left(p+4\right)$$  

• $$\left(4p^2+3\right)\left(p+2\right)$$  

• $$\left(4p^2+8p\right)\left(3p+6\right)$$  

Multiple Choice

What is the "formula" for finding the axis of symmetry? 

• $$y=ax^2+bx+c$$  

• $$x=\frac{-b}{2a}$$  

• $$y=mx+b$$  

• $$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$  

Quadratic Unit Test Concepts

• Vertex and Axis of Symmetry

• Real World quadratic functions

• Quadratic vertex form

• Quadratic standard form

• Quadratic factored form

• Factoring trinomials

• Difference of Two Squares

• Factoring 4 terms by grouping