Unit 7 Review

Quadratic Functions Review

Complete this for bonus points on your test. Watch the videos for extra help if needed.

Multiple Choice

What are the green dots called?

• axis of symmetry
• vertex
• parabola
• roots or x-intercepts

Multiple Choice

What is the equation for axis of symmetry?

• y=3
• x=3
• x=5
• x=1

Multiple Choice

If we have the equation y=ax²+bx+c, how can we can find the x-coordinate of the vertex?

• -a
• -b/a
• b/2a
• -b/2a

Multiple Choice

Which of the following equations matches standard form of a quadratic?

• ax + by = c
• y = a(x - h)² + k
• y = ax² + bx + c
• y = mx + b

Multiple Choice

If I want to find out when an object hits the ground, I should _________.

• Use x = (-b/2a) as my answer.
• Set my equation = 0 and solve.
• Replace x with 0 and evaluate.
• Find the y-coordinate of the vertex.

Multiple Choice

What is the range of this function?

• (- ∞,+∞)
• [0, +∞)
• [-2, +∞)
• [2, +∞)

Multiple Choice

What are the
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

y = 5(x+2)(x-1)

• Standard
• Vertex
• Factored
• None of These

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

Identify the vertex and whether the graph opens up or down.

• (-1, 4); opens up
• (-1, 4); opens down
• (1, 4); opens up
• (1, 4); opens down

Multiple Choice

What is the vertex of
f(x) = 2(x - 5)² + 12

• (-5, -12)
• (5,-12)
• (5, 12)
• (-5, 12)

Multiple Choice

Which form is the equation
y = -3(x-5)²+7 in?

• Standard
• Vertex
• Factored
• None of These

Multiple Choice

Find the vertex of 
f(x) = -x² - 4x + 12

• (-2, 16)
• (2, 0)
• (2, 4)
• (-2, 4)

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

What is the y intercept for the equation:
y = -8x² + 3x - 7

• (0, -8)
• (0, 3)
• (0, 7)
• (0, -7)

Multiple Choice

What form is the equation in?
y = 2x²-8x+7

• Standard
• Vertex
• Factored
• None of These

Multiple Choice

What does "a" control in a graph of f(x) = ax²+ bx+ c?

• Opens up or down
• Where the graph crosses at X-intercept
• Where the graph crosses at Y-intercept

Multiple Choice

What are the x- intercepts?

• x= 0 and x= -4
• x= 0 and x= 4
• y= 0
• x= 2

Multiple Choice

What is another word for zeros?

• y-intercepts
• roots
• vertex
• axis of symmetry

Multiple Choice

Which answer choice describes  y = -3x² +7x - 2 accurately?

• opens up with a maximum
• opens up with a minimum
• opens down with a maximum
• opens down with a minimum 

Multiple Choice

Does this graph in the back have maximum or minimum value?

• maximum
• minimum
• neither
• both

3 Methods to Find the x-intercepts (solutions, roots, zeros) of quadratic equations.

Solving Quadratic Equations by Factoring

Make sure they are set =0. If a is larger than 1 see if there is a GCF- if so take it out. Then factor using snowflake method. Solve for each ( ).

Refresher on Factoring using Snowflake Method

Multiple Choice

The solutions of the quadratic equation

x²+2x-15=0 are (hint: find the zeros) FACTOR

• x = 3 or x = 5

• x = 5 or x = -3

• x = -5 or x = 3

• x = -3 or x = -5

Multiple Choice

Which is the correct graph of the function:

Multiple Choice

Convert x² - 9x + 20 to factored form and solve.

• (x-10)(x+2); x = -2, 10
• (x+4)(x+5); x = -5, -4
• (x-4)(x-5); x = 4, 5
• Not factorable

Multiple Choice

Solve:
x² - 49 = 0

• x = -7, x = 7
• x = -7
• x = 7
• x = -7, x = 1

Multiple Choice

What is the first question you ask yourself when factoring a polynomial? 

• How many terms does it have? 
• Is there a GCF? 
• What strategy should I use? 
• Why do I have to learn this?!?!?!

Multiple Choice

Factor x²-16

• (x+4)²

• (x-4)²

• (x-16)(x+16)

• (x-4)(x+4)

Solving Quadratics by Completing the Square

Remember: It gives you your y-int, vertex, and x-intercepts. However, it is a lot of steps. Just be familiar with the steps.

Multiple Choice

What should be added to both sides of the following equation to complete the square?
x² + 12x = 5

• 12
• 6
• 36
• 5

Multiple Choice

Complete the square for
x² + 12x + ____

• x² + 12x + 144
• x² + 12x + 36
• x² + 12x - 36
• x² + +12x - 144

Multiple Choice

What is one of the solutions to this equation?
(2x - 1)² = 49

• 7
• -7
• -4
• -3

Multiple Choice

When do you use the plus or minus symbol?
±

• After taking the square root of both sides
• After adding the square to both sides
• After taking half of b
• After setting the equation equal to zero

Multiple Choice

When factoring
x² - 4x + 4 = 20,
what goes in the blank?
(x - __ )² = 20

• 4
• 2
• 8
• 20

Multiple Choice

What is the first step to solving THIS equation by completing the square?
a² + 10a + 21 = 0

• Set the equation equal to zero
• Divide 10 by 2 and add the result to both sides
• Add a² and 10a together
• Subtract the 21

Multiple Choice

What do you do to the b value to correctly complete the square?

• square it
• divide it by 2 and square the result
• divide it by 2 and take the square root of the result
• divide it by 2 only

The last method of finding your x-intercepts is Quadratic Formula.

This is easy to use and will give you an answer no matter if it is rational or irrational.

Multiple Choice

What should you do first in solving this equation?

x² + 6x - 13 = 3

• Factor

• Write down: a = 1, b = 6, c = -13

• Subtract 3 from both sides.

• Add 3 to both sides.

Multiple Choice

Use the quadratic formula to find the solutions for

y = -x² - 5x + 12

• No Real Solution

Multiple Choice

Use the quadratic formula to solve 2x² + 2x - 12.

• -2, 3

• 2, 3

• 2, -3

• -2, -3

Multiple Choice

Determine the values of a, b, and c for the quadratic equation:

4x² – 8x = 3

• a = 4, b = -8, c = 3

• a = 4, b =-8, c =-3

• a = 4, b = 8, c = 3

• a = 4, b = 8, c = -3

The discriminant

• part of the quadratic formula found under the radical

• tells you how many solutions (x-intercepts) your equation will have.

Multiple Choice

If the Discriminate is equal to 0, it has how many roots?

• 0

• 1

• 2

• 3

Multiple Choice

If the Discriminate is greater than 0 it has how many roots?

• 0

• 1

• 2

• 3

Multiple Choice

What is the discriminant of 6x² − 2x − 3 = 0

• 76

• 29

• 68

• none of these

Multiple Choice

____________
For the function above, is the discriminant positive, negative, or zero?

• Positive
• Negative
• Zero
• Not Sure

Multiple Choice

The discriminant is

• aX²  + bX  +  c
• b - 4ac
• b² - 4ac
• b² + 4ac

Quadratic Word Problems

• Area problems

• Projectile Motion

Multiple Choice

You are building a rectangular wading pool. You want the area of the bottom to be 108 ft². You want the length of the pool to be 3 ft longer than it's width. What will the dimensions of the pool be?

SET UP YOUR LET STATEMENTS and EQUATION!! Then SOLVE.

• 36 feet and 3 feet

• 9 feet and 6 feet

• 12 feet and 15 feet

• 12 feet and 9 feet

Multiple Choice

Your nephew is standing on his deck, which is 4 feet off the ground. He tosses his toy up into the air. The equation

h = -2t² + 7t + 4 models the toy's height, h, from the ground at t seconds after he threw it. How high is the toy after 1 second?

• 2

• 4

• 9

• 10

• 15

Multiple Choice

A ball is thrown into the air with an upward velocity of 40ft/s. Its height h in feet after t seconds is given by the function :

h(t) = -16t² + 40t + 10

How many seconds does it take the ball to reach its maximum height?

• 1.25 seconds

• 1.4 seconds

• 2.5 seconds

• 2 seconds

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

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

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