Quadratic Functions End of Unit Review

.Quadratic Functions

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Multiple Choice

What do we call the graph of a quadratic function?

• parabola
• linear
• cubic
• sinusoidal

Multiple Choice

What are the

roots (x-intercepts) of the function

f(x)= (x - 2)(x + 3)?

• x = - 2 or x = 3

• x = 2 or x = -3

• The are no real roots

• x = 2 or x = 3

Multiple Choice

What is the vertex of this function?

• (0, -3)

• (1, -4)

• (-2, 5)

• {-1, 3}

Multiple Choice

If given the equation

y = 3(x + 5)² - 4, what is the vertex of the parabola?

• (5, -4)

• (-5, -4)

• (-15, -4)

• (15, -4)

Multiple Choice

What is the vertex of

f(x) = 2(x - 5)² + 12

• (-5, -12)

• (5,-12)

• (5, 12)

• (-5, 12)

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 axis of symmetry for the following equation?

y=4x²-8x+9

• x=-8

• x=1

• x=-1

• x=2

Multiple Choice

Does the following quadratic equation have a maximum or minimum value? How can you tell?

y=x²+2x-3

• Minimum value, because the a value is positive

• Maximum value, because the b value is positive

• Maximum value, because the a value is positive

• Minimum value, because the c value is negative

Key Features

• Vertex

• X - intercept/roots/zeros

• Y - intercept

• Max or Min

• Axis of symmetry

Fill in the Blank

What is the vertex of the function? Write your answer as an ordered pair (x,y) with no spaces.

(

,

)

Multiple Select

Does the graph have a max or a min and what is the value? (Select 2 answers)

• Max

• Min

• -1

• 1

Domain & Range

• For quadratic functions, THE DOMAIN IS ALWAYS -INF,INF

• Range depends on the min/max

Multiple Choice

What is the range of the graph?

• $$\left(-\infty,\infty\right)$$

• $$\left(-\infty,0\right)$$

• $$\left(0,\infty\right)$$

Multiple Choice

What is the domain of the graph?

• $$\left(-\infty,\infty\right)$$  

• I wasn't paying attention to what Mr. Chimbora just said on the last slide

Examples!

Multiple Choice

Question 1

• A

• B

• C

• D

Multiple Choice

Question 2

• A

• B

• C

• D

Multiple Choice

A line about which a figure is symmetric is the:

• Solution Set
• Intercept Formula
• Quadratic Function
• Axis of Symmetry

Multiple Choice

What is the Axis of symmetry?

• Y=3
• y=-3
• x= 3
• x=-3

Multiple Choice

Use the picture to find  the vertex and axis of symmetry

•  Vertex (3,8) Axis x=3
• Vertex (3,8) Axis y=3
• Vertex (8,3) Axis x=3
• Vertex (8,3) Axis y=3

Multiple Choice

What are the x- intercepts (roots, solutions)?

• x= 0 and x= -4

• x= 0 and x= 4

• y= 0

• x= 2

Multiple Choice

Does this parabola have a minimum or maximum and what is its value?

• minimum: 2

• maximum: 2

• minimum: 5

• maximum: 5

Forms of Quadratic Functions

Multiple Choice

Identify the form of the quadratic function:
f(x)=(x+1)²-3

• Quadratic
• Standard
• Factored
• Vertex

Multiple Choice

Identify the form of the quadratic function:
f(x)=3(x+2)(x-1)

• Quadratic
• Standard
• Factored
• Vertex

Factored Form of a Quadratic Function

Multiple Choice

Identify the form of the quadratic function: f(x)=2x²+4x+1

• Quadratic
• Standard
• Factored
• Vertex

Multiple Choice

Elaine shoots an arrow upward at a speed of 32 feet per second from a bridge that is 28 feet high. The height of the arrow is given by the function h(t) = -16t² + 32t + 28, where t is the time in seconds. What is the maximum height that the arrow reaches?

• A. 24 ft.

• B. 30 ft.

• C. 44 ft

• D. 32 ft.

Multiple Choice

What can we find easily in standard form?

• vertex
• zeros/x-intercepts
• y-intercept

Multiple Choice

Does the equation open or or down? 
Y = -3x² +7x - 2

• up
• down

Multiple Choice

What are the roots of the function
f(x)= (x - 2)(x + 3)?

• x = - 2 or x = 3
• x = 2 or x = -3
• The are no real roots
• x = 2 or x = 3

Multiple Choice

Determine the number of solutions to the given linear-quadratic system.

• 0 solutions
• 1 solution
• 2 solutions
• 3 solutions

Multiple Choice

Determine the solution to the given linear-quadratic function.

• (0, 0)
• (3, 0)
• (2, -3)
• (-3, 2)

Multiple Choice

Two equations were graphed on the set of axes below.  Which point is a solution to the system of equations ?

• (0,3)
• (5,0)
• (2,-3)
• (8,9)

Multiple Choice

How many solutions does this system of equations have?

• one solution

• two solutions

• no solution

• infinitely many solutions

Multiple Choice

Determine the solution to the given linear-quadratic function.

• (0, 0)
• (3, 0)
• (2, -3)
• (-3, 2)

Multiple Choice

Which of the following graphs correctly represents:

y=x²

y=-2x+1

Multiple Choice

Based on the table, which function can best be used to model this situation?

• h(t) = 99t² + 858

• h(t) = -4.9t² + 295t + 0.6

• h(t) = -4.9t² + 295t + 2

• h(t) = 99t² + 1,470.3

Multiple Choice

Which of the following quadratic equations best represents the following data?

• y = 7x² - 3x

• y = 3x² - 2x + 1

• y = 6x² + 3x - 2

• y = 7x² - 3x + 1

Multiple Choice

Find the quadratic regression equation for the relationship of the horizontal distance and the height of the ball in the provided table.

• $$-18x^2+2.11x+4.21$$
  

• $$-0.06x^2+1.06x+7.9$$
  

• $$-6x^2+1.06x+79$$
  

• $$-0.12x^2+2.11x+4.22$$

Scenario 10

Multiple Select

How do I find…

When an object hits the ground? (circle all that apply)

A: use the axis of symmetry formula

B: use the Zero function

C: use the axis of symmetry formula, plug back into equation

D: Use the Quadratic Formula

E: use the Value function

• use the axis of symmetry formula

• use the Zero function

• use the axis of symmetry formula, plug back into equation

• Use the Quadratic Formula

• use the Value function

Multiple Choice

Which of the following is the standard form of $$f\left(x\right)\ =\ \left(3x\ +\ 2\right)\left(2x\ -\ 4\right)$$ ?

• $$f\left(x\right)\ =\ 3x^2+4x\ -\ 4$$

• $$f\left(x\right)\ =\ 3x^2+16x-8$$

• $$f\left(x\right)\ =\ 3x^2-8x-8$$

• $$f\left(x\right)\ =\ 3x^2-12x-4$$