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Vocabulary
Transformations of Quadratic Functions
Min/Max and Intercepts
Converting Between Forms
Quadratic Word Problems
100

The shape of a quadratic function is called this

What is a Parabola?

100

Describe the transformation in the quadratic function.

y=x2+8

Up 8.

100

Does the function below have a minimum or a maximum? And, what is the y-intercept?

f(x)=4x2+6x−5

Minimum.

y-intercept=−5.

100

Re-write the quadratic function below in Standard Form.

y=4(x+7)(x+2)

y=4x2+36x+56

100

A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation. Using this equation, find out the time at which the rocket will reach its max, to the nearest 100th of a second.

y=−16x2+241x+119


x=7.53 seconds (time at max)

200

The line that cuts a parabola in half

What is the axis of symmetry?

200

Describe the transformation in the quadratic function.

y=3x2

Vertical stretch.

200

Does the function below have a minimum or a maximum? And, what is the y-intercept?

f(x)=3x2−9x+4

Minimum.

y-intercept=4.

200

Re-write the quadratic function below in Standard Form.

y= −5(x−3)(x+6)

y=−5x2−15x+90

200

A company sells widgets. The amount of profit, y, made by the company, is related to the selling price of each widget, x, by the given equation. Using this equation, find out what price the widgets should be sold for, to the nearest cent, for the company to make the maximum profit.

y=−x2+83x−620

x=$41.50 (best price)

300

The highest or lowest point of a quadratic function.

What is a vertex?

300

Describe the transformations in the quadratic function.

y=3/2x2+7

Vertical stretch by 3/2

Up 7

300

Does the function below have a minimum or a maximum? And, what is the y-intercept?

f(x)=−2x2+8x+1

Maximum.

y-intercept=1.

300

Re-write the quadratic function below in Standard Form.

y= −9(x+1)(x−9)

y=−9x2+72x+81

300

A company sells widgets. The amount of profit, y, made by the company, is related to the selling price of each widget, x, by the given equation. Using this equation, find out the maximum amount of profit the company can make, to the nearest dollar.

y=−35x2+1038x−4878

y=$2818→Max profit

400

What type of function has a highest power of 2?

What is a quadratic function?

400

Describe the transformation in the quadratic function.

y=(x+6)2+4

Left 6

Up 4

400

Does the function below have a minimum or a maximum? And, what is the y-intercept?

f(x)=5x2−10x+7

Minimum.

y-intercept=7.

400

Put the quadratic into vertex form and state the coordinates of the vertex.

y=x2−6x−7

y=(x−3)2−16

Vertex =(3,−16)

400

A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation. Using this equation, find the time that the rocket will hit the ground, to the nearest 100th of second.

y=−16x2+261x+146

x=16.85 seconds.

500

What are two other names for the x-intercepts on a quadratic function?

What is roots and zeros?

500

Describe the transformation in the quadratic function.

y=(x−3)2−6

Right 3 

Down 6

500

Does the function below have a minimum or a maximum? And, what is the y-intercept?

f(x)=−x2+4x−3

Maximum.

y-intercept=−3.

500

Put the quadratic into vertex form and state the coordinates of the vertex.

y=x2−8x−33

y=(x−4)2−49

Vertex =(4,−49)

500

A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation. Using this equation, find out the time at which the rocket will reach its max, to the nearest 100th of a second.

y=−16x2+111x+50

x=3.47 seconds (time at max)