Characteristics of Quadratics

Characteristics of Quadratics

Let's Review for the Test!

Standard Form of a Quadratic Function

f(x) = ax² + bx + c

Multiple Choice

The graph of a quadratic function is called a

• Parabola

• Vertex

• Axis of Symmetry

• Vertex Form

Multiple Choice

3x² - 4 is a quadratic

• true

• false

Multiple Choice

What direction is the following equation opening?

y=-3x²-7x+8

• Up

• Down

• Left

• Right

Multiple Choice

Does

y = -4x²

have a maximum or minimum value?

• maximum

• minimum

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 

How can you identify the y-intercept?

In an equation?

On a graph?

Multiple Choice

What is the y-intercept of this parabola?

• (−1, 3)

• (−3, 11)

• (−2, 5)

• (0, 5)

Multiple Choice

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

• (0, -8)
• (0, 3)
• (-8, -7)
• (0, -7)

Multiple Choice

What is the y-intercept of the function y=-2x²+8x-6?

• (0, 8)
• (0, -6)
• (0, 2)
• (0, 0)

How can you identify the x-intercept(s)?

In an equation?

On a graph?

What are the steps to mathematically finding the x-intercepts of a quadratic?

Multiple Choice

What are the x- intercepts?

• x= 0 and x= -4

• x= 0 and x= 4

• y= 0

• x= 2

Multiple Choice

Solve

2x² - 3x - 2 = 0

• x = 1, x = -1

• x = -1/2, x = 2

• x = 1/2, x = 2

• x = 1/2, x = 1

Multiple Choice

What is another word for ROOTS?

• Zeros

• y-intercept

• Maximum

• Vertex

Multiple Choice

Find all the solutions for x when

x² + 9x - 36 = 0

• (x + 12)(x - 3)

• x = 12 and x = -3

• x = -12 and x = 3

• (x - 9)(x - 4)

Multiple Choice

What are the zeros of (2x+5)(x-6)=?

• -6, 5/2

• -5/2, 6

• 6, 2

• 5, -6

Multiple Choice

How many zeros does this parabola have?

• 3

• 2

• 0

• 1

Multiple Choice

What are the solutions of the following equation:

 $4x^2-20x=-16$  

Hint:  Put the equation into standard form first  $a^2+bx+c=0$  
Then factor the equation and use the Zero-Product Property.

• x = 1 and x = 4

• x = -16 and x = 20

• x = - 4 and x = 16

What is the vertex of a Quadratic Function?

How do you identify it on a graph?

How do you identify it in an equation?

Multiple Choice

Find the vertex of

f(x) = -x² - 4x + 12

• (-2, 16)

• (2, 0)

• (2, 4)

• (-2, 4)

Multiple Choice

Does this graph have a maximum or minimum value?

• maximum

• minimum

• neither

• both

Multiple Choice

What is the vertex?

• (2, 4)

• (3, -1)

• (0, 8)

• (4, 2)

Multiple Choice

Find the vertex of f(x)= -2x²-16x+3.

• (4, -93)

• (-4, 35)

• (-4,99)

• (8,3)

Multiple Choice

Find the vertex. y = x²+ 16x + 71

• V(-8, 7)

• V(-8, 3)

• V(8, 10)

• V(16, -2)

Remember: Parabolas are symmetrical. They have a line of symmetry.

How do we identify that on a graph?

How do we identify that mathematically?

Multiple Choice

What is the axis of symmetry?

• x = - 4

• x = - 2

• x = 0

• x = 4

Multiple Choice

The axis of symmetry of this parabola is...

• y = 4

• y = -4

• x = 4

• x = -4

Multiple Choice

What's the axis of symmetry of y = 3x² - 6x + 4

• x=1

• x=-6

• x=2

• x=-1

Multiple Choice

Find the axis of symmetry for

f(x) = x²- 8x + 15.

• x = -4

• x = 4

• y = 4

• y = -4

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?

• the slope of the graph
• the dividing line for a parabola
• a way to spin my pencil
• the x-axis

Quadratic Function Word Problems

Multiple Choice

You are cliff diving with some friends. Your path to the water is modeled by h(t) = -16t^2 + 8t +24. How long will it take for you to hit the water? What are you solving for?

• roots

• axis of symmetry

• y-value of the vertex

• y-intercept

Multiple Choice

Your younger sibling is standing on his deck, which is 4 feet off the ground. They toss their toy up into the air. The toy's height, h, from the ground at t seconds after they threw it is modeled by the function h(t) = -2t² + 7t + 4. How long does it take the toy to hit the ground?

• .5 sec

• 2 sec

• 4 sec

• 8 sec

Multiple Choice

If a toy rocket is launched from the ground and its height h after t seconds is given by the function h(t) = -8t² +64t.

When will the object reach its maximum height?

• 128 ft

• 0 seconds

• 0 ft

• 4 seconds

Multiple Choice

The height of a ball that is thrown into the air is given by h(t) = -5t² + 40t + 2. From what height was the balloon released?

• 2 meters

• 4 meters

• 5 meters

• 8 meters

Multiple Choice

A ball is thrown into the air. Its height in feet after t seconds is given by the function h(t) = –5t² + 20t. How high will the ball be after 3 seconds?

• 20 ft

• 15 ft

• 5 ft

• 10 ft

Multiple Choice

A dolphin jumps from the water. The function h(t) = -16t² + 80t models the dolphin's height at any given time, t. What is the maximum height the dolphin jumps? What are you solving for?

• solutions

• y-intercept

• axis of symmetry

• y-value of the vertex

Multiple Choice

A ball is thrown downward from a window in a tall building. Its position at time t in seconds is s(t) = 16t² + 32t where s is in feet. How long (to the nearest tenth) will it take the ball to fall 224 feet?

• 2.7 sec.

• 8.4 sec.

• 3.7 sec.

• 2.9 sec.