Vocabulary
The shape of a quadratic function is called this
What is a Parabola?
Describe the transformation in the quadratic function.
y=x2+8
Up 8.
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.
Re-write the quadratic function below in Standard Form.
y=4(x+7)(x+2)
y=4x2+36x+56
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)
The line that cuts a parabola in half
What is the axis of symmetry?
Describe the transformation in the quadratic function.
y=3x2
Vertical stretch.
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.
Re-write the quadratic function below in Standard Form.
y= −5(x−3)(x+6)
y=−5x2−15x+90
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)
The highest or lowest point of a quadratic function.
What is a vertex?
Describe the transformations in the quadratic function.
y=3/2x2+7
Vertical stretch by 3/2
Up 7
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.
Re-write the quadratic function below in Standard Form.
y= −9(x+1)(x−9)
y=−9x2+72x+81
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
What type of function has a highest power of 2?
What is a quadratic function?
Describe the transformation in the quadratic function.
y=(x+6)2+4
Left 6
Up 4
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.
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)
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.
What are two other names for the x-intercepts on a quadratic function?
What is roots and zeros?
Describe the transformation in the quadratic function.
y=(x−3)2−6
Right 3
Down 6
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.
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)
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)