Intro to Quadratics

Intro to Quadratic Functions

Multiple Choice

The graph of a quadratic function is called a

• Parabola
• Vertex
• Axis of Symmetry 
• Vertex Form

Multiple Choice

What is the quadratic parent function?

• $$y=x$$  

• $$y=10^x$$  

• $$y=x^2$$  

Multiple Choice

Is the graph of the equation y=2x² wider, narrower or the same width as the standard parabola y = x²?

• wider

• narrower

• same

• impossible to tell

Multiple Choice

Which quadratic would be the narrowest?

• $$f\left(x\right)=\frac{1}{2}x^2$$

• $$f\left(x\right)=x^2$$

• $$f\left(x\right)=3x^2$$

• $$f\left(x\right)=5x^2$$

Multiple Choice

If the blue graph is f(x) = x²

then the red must be...

• g(x) = x² - 5

• g(x) = x² + 5

• g(x) = (x - 5)²

• g(x) = (x + 5)²

Multiple Select

What are the other names for the "solution(s)" to a quadratic equation?

**Select all that apply!**

• root(s)

• x-intercept(s)

• zero(s)

• y-intercept(s)

Multiple Choice

Use the graph to determine the X-intercepts:

• (-1,0) and (-3,0)

• (1,0) and (3,0)

• (0,1) and (0,3)

• (0,-1) and (0,-3)

Multiple Choice

How many zeros does this parabola have? 

• 3
• 2
• 0
• 1

Multiple Choice

Use the graph to determine the solutions.

• -1 and -3
• 1 and -3
• 1 and 3
• -1 and 3

Multiple Choice

What is another name for the x-intercepts of a quadratic?

• y-intercept
• Zeros
• x-axis
• They don't have another name

Multiple Choice

What is this formula?

• This is the speed of light formula.
• This is the quadratic formula.
• This is the zero product property.
• This is scary.

Multiple Choice

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

• minimum: 2

• maximum: 2

• minimum: 5

• maximum: 5

Multiple Choice

Does this graph have a maximum or a minimum?

• maximum

• minimum

• I am not sure.

• neither

Multiple Choice

Determine the domain and range of the function

• Domain: All real numbers

  Range: All real numbers

• Domain: x ≥ -4

  Range: All real numbers

• Domain: All real numbers

  Range: y ≥ -4

• Domain: -1 ≤ x ≤ 5

  Range: y ≥ -4

Multiple Choice

What is the green dashed line called?

• roots or x-intercepts
• parabola
• axis of symmetry
• line of dashes

Multiple Choice

Which value is the vertex?

• (-4, 0)

• (-1, -9)

• (0, -8)

• (2, 0)

Multiple Choice

What is the equation for the axis of symmetry?

• x = 2

• x = 6

• x = 3

• x = 0

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 is the vertex of the quadratic function:

f(x) = x² - 6x + 11

Hint: Use Desmos

• (3,2)

• (-3,-2)

• (-3,2)

• (3,-2)

Multiple Choice

Use the picture to find the vertex and axis of symmetry.

• Vertex: (8, 3); axis of symmetry: y=3

• Vertex: (8, 3); axis of symmetry: x=3

• Vertex: (3, 8); axis of symmetry: y=3

• Vertex: (3, 8); axis of symmetry: x=3

Multiple Choice

What is the vertex for
f(x)=4(x-2)² + 3

• (-2, 3)
• (2,-3)
• (4,3)
• (2,3)

Multiple Choice

Which equation has a vertex of (-3, 4)?

• y = 2(x+3)² + 4
• y = (x+3)² - 4
• y = (x-3)² + 4
• y = 2(x - 3)² + 4

Multiple Choice

A fountain shoots water in an arc over a lake that can be modeled by the graph of the equation y= -0.4x² + 8x where x is the horizontal distance (in feet) from the fountain base and y is the height (in feet) above the river.  How high does the water go?

• It goes 11.78 feet high
• It goes 20 feet high
• It goes 40 feet high
• It goes 10 feet high

Multiple Choice

A raft is dropped from a helicopter 256 feet in the air above the ocean.  Its approximate height, h, after t seconds is given by the function h(t) = -16t² + 256.  How many seconds did it take the raft to hit the water? 

• -4
• 2
• 4
• 8

Multiple Choice

What is the initial (starting) height of an object following this path?  h(t) = -16t² +20t + 6

• -16 feet 
• 0 feet
• 20 feet 
• 6 feet 

Multiple Choice

If the graph shows price vs profit, what is the maximum profit? 

• 35
• 12,000
• 12,500
• 60

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

A lizard is jumping across the water in search of food. The equation h = -12t² + 6t models the lizard's height in feet above the water t seconds after he jumps. How long after jumping is he back on the water?

• 0.1 seconds

• 0.25 seconds

• 0.50 seconds

• 0.75 seconds

• 1 second

Multiple Choice

If a toy rocket is launched vertically upward from ground level with an initial velocity of 128 feet per second, then its height h after t seconds is given by the equation
h(t) = -16t² +128t  
When will the object reach its maximum height?

• 4 ft
• 0 seconds
• 0 ft
• 4 seconds