Features
Vertex Form
Standard Form
Modeling
Linear, Quad, or Exp?
100
What is the shape of this graph?
The shape is a parabola.
100
What is the formula for vertex form? Hint: f(x) = ???
f(x) = a(x - h)2 + k
100
What is the formula for a standard form quadratic function. f(x) = ???
f(x) = ax2 + bx + c
100
Calculate the residuals for the actual and predicted y in the chart.
Is this quadratic function a good fit for the data?
Yes, the function is a good fit because there are positive and negative residuals.
100
If you find that the 2nd differences of y-values for a function are the same, then the function can be modeled with a _________ function.
quadratic
200
What is the point in the center of the parabola called? It is shown here in black.
The point is the vertex.
200
Identify a, h, and k in the function f(x) = 3(x - 2)2 + 4
a = 3
h = 2
k = 4
200
Find the axis of symmetry and y-intercept for the function f(x) = x2 + 8x - 7
Axis of symmetry: x = -4
y-intercept: (0, -7)
200
Write a quadratic function in standard form to model the area of the painting. Hint: Multiply the height by the width.
f(x) = 2x2 + 13x + 20
200
What type of function can be used to model this data? Why?
A linear function because the first differences are the same.
300
What is the line down the center of the parabola called? It is shown here as x = 3.
The line down the center of the parabola is the axis of symmetry.
300
What are the vertex and axis of symmetry of the function f(x) = 0.5(x + 4)2 + 7
vertex = (-4, 7)
axis of symmetry, x = -4
300
Change the function f(x) = -2(x - 3)2 - 5 into standard form.
What is the y-intercept?
f(x) = -2x2 + 12x - 23
y-intercept: (0, -23)
300
Write a vertical motion model in the form h(t) = -16t2 + v0t + h0 for the situation below:
Teddy kicks a soccer ball with an initial velocity of 32 f/s and an initial height of 0 ft
)
h(t) = -16t2 + 32t
300
What type of function best models the data shown? Why?
An exponential function because the ratios of y-values are the same
400
What is the point called where the parabola crosses the y-axis? Hint: It is shown here at (0, 5).
The point is the y-intercept.
400
What is the function in vertex form for the parabola shown?
f(x) = 2(x - 3)2 - 4
400
What is the function for this graph in standard form?
f(x) = -x2 - 6x - 10
400
Marco has a 12 ft by 12 ft patio. He wants to enlarge it by x feet on three sides as shown. Write a function in standard form to model the size of the patio in square feet.
f(x) = 2x2 + 36x + 144
400
Which type of function best models the data shown? Why?
Quadratic function, because the second differences are the same.
500
What are the points where the parabola crosses the x-axis called? There may be none, one, or two of these points. They are shown here at (-3, 0) and (4, 0)
The points are the roots.
500
Graph the function f(x) = -0.5(x + 2)2 + 1 and identify the axis of symmetry.
Axis of Symmetry: x = -2
500
Graph the function f(x) = -x2 + 10x + 20
What is the vertex?
Vertex: (5, 5)
500
Write a function using h(t) = -16t2 + v0t + h0 to model the vertical motion of an object with an initial vertical velocity of 48 ft/s and initial height of 10 feet.
Will the object hit the ceiling in a stadium that is 50 feet high?
h(t) = -16t2 + 48t + 10
No, the object's maximum height is only 46 feet.
500
Which type of function best models the data shown? Write a function to fit the data.
A linear function is the best fit.
The function that models the data is f(x) = 7x - 9