Features
Vertex Form
Exponential
Absolute
Value
Value
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 an exponential function?
What is y=abx or f(x) =abx
100
In the following equation, what is the value of a?
y=|x-2|-4
What is 1 or 1/1?
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
What is the initial value of the following function?
f(x)= 3(1/2)x
What is 3?
200
In the following equation, will the graph open upwards or downwards?
y=-|x|+3
What is downwards?
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
Does the following function represent exponential growth or decay?
g(x)= 2(2/3)x
What is exponential decay?
300
In the following equation, what is the vertex?
y=|x+1|-9
What is (-1,-9)?
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 asymptote of the function?
h(x)= -8(2.5)x -3
What is -3?
400
In the following equation, what is/are the x-intercept(s)?
y=-|x-1|+1
What is 1?
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
What is the range of the following function?
f(x)= 5x+2
What is y>2?
500
In the following equation, what is the vertex?
y=|x-2|-4
What is (2,4)?
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