Forms of Quadratics
Attributes of Graphs
Applying Quadratics
Misc./RANDOM
100
What is the vertex form of this quadratic function?
y = x2 – 6x + 8
y = (x – 3)2 - 1
100
Does this graph have a maximum or minimum and at what value?
minimum of -1
100
The height of a rocket that Spencer launched is represented by the function h = -2t2 + 8t, where h is the height of the rocket, and t is the time in seconds. When does the rocket reach its maximum?
2 seconds
100
What is the y-intercept of the following quadratic function?
y = 3(x + 3)2 – 15
(0, 12)
200
What is standard form equation of the following quadratic function?
Y = -2(x + 1)2 + 2
y = -2x2 – 4x
200
The graph of the equation y = -2x2+ 4x is shown below. For what value or values of x is y = 0?
x = 0 and x = 2
200
The height of a rocket that Spencer launched is represented by the function h = -2t2 + 8t, where h is the height of the rocket, and t is the time in seconds. How long does the rocket remain in the air?
4 seconds
200
What value is needed to complete the square?
x2 - 16x = 20
64
300
g(x) = x2 + 5x + 6
Where is function g(x) equal to zero?
Also write in Factored Form.
{-3,-2}
g(x)=(x+3)(x+2)
300
What is the average rate of change from x=-2 to x=1 of the following?
f(x) = -x2 – 2x
-1
300
Frank and Grant, twins in 8th grade, launched two different rockets into the air. Their paths are modeled by the quadratic functions below. Which rocket went higher and by how much?
Frank: f(x) = -(x – 20)2 + 100
Grant: f(x) = -7(x – 24)2 + 75
Frank by 25 ft.
300
Describe the transformation or transformations of the following quadratic equation compared to the parent graph y = x2.
y = -(x + 2)2 - 4
reflection over x-axis, left 2, down 4
400
Write a vertex form equation for a quadratic that has a vertex of (2,5) and passes through the point (0,9).
y=(x-2)2+5
400
What is the domain? What is the range?
(written in both formats)
Domain:all real numbers or (-∞,∞)
Range: y > -1 or [-1, ∞)
400
Write a TRUE statement about the situation involving domain and range and vertex.
answers will vary
400
What is the average rate of change over the interval [1, 4] of this quadratic function?
-1
500
Write a standard form equation for the graph below.
y=-2x2-4x+4
500
Describe the transformation or transformations of the following quadratic equation compared to the parent graph y = x2.
y = - 3(x – 4)2 + 2
reflection over x-axis, stretch of 3, right 4, and up 2
500
Tony punted a football during practice and the table below shows the horizontal distance compared to the height of the football. Find an equation that represents the situation in standard form and predict the height when the football is 75ft away.
y= -0.05x2+5x+1
94.75 feet
500
Create an equation that represents a parabola with the same vertex as y = 3(x + 3)2 – 15 but opens in the opposite direction.
y = - #(x + 3)2 – 15 … any -# in the front will work