Function Features
Vertex Form
Standard Form
Modeling
Linear, Exponential or Quadratic?
100
What is the graph of a quadratic function called?
parabola
100
What is the vertex form of any quadratic function?
f(x)=a(x-h)^2+k
100
What is the standard form of any quadratic function?
f(x)=ax^2+bx+c
100
The function below models the height h, in feet, of a ball t seconds after it is thrown straight up into the air. What is the initial velocity and initial height of the ball?
h(t)=-16t^2+32t+24
initial velocity is 32 ft/second
initial height is 24 feet
100
What is the first step in determining whether a table shows a linear, quadratic, or exponential function?
Determine if the differences in the x-values are constant.
200
Is the graph of this function narrower or wider than the parent function?
g(x)=1.5x^2
narrower
200
The vertex form of a function helps you identify the vertex as well as this other parabola feature.
axis of symmetry
200
The standard form of a quadratic function helps you find the axis of symmetry, x-coordinate of the vertex as well as this other feature of a parabola.
y-intercept
200
The function below models the height, in inches, of a frog t seconds after it jumps. What is the maximum height of the jump?
f(t)=-16t^2+32t
16 inches
200
Does this set of data represent a linear, quadratic or exponential function?
exponential
300
What is the name of the point on a parabola that is either the maximum or minimum point of the function?
vertex
300
Identify the vertex for this function.
g(x)=4(x+8)^2+1
(-8,1)
300
What is the y-intercept of the following function?
f(x)=-3x^2+12x+5
(0,5)
300
Write a quadratic function to represent the area of the rectangle.
f(x)=2x^2+9x-5
300
Does this set of data represent a linear, quadratic or exponential function?
linear
400
Describe two similarities and two differences of these functions.
Similarities: same axis of symmetry, same vertex
Differences: opens different directions, g(x) is wider
400
Identify the axis of symmetry for the function:
y=-(x-5)^2-2
x=5
400
What is the axis of symmetry of this function?
f(x)=-x^2+4x+5
x=2
400
For the vertical motion model below, identify the maximum height reached by an object and the amount of time the object is in the air to reach the maximum height. Round to the nearest tenth.
h(t)=-16t^2+54t+3
Maximum height: 48.6 feet
Time to reach maximum height: 1.7 seconds
400
Does this set of data represent a linear, quadratic or exponential function?
quadratic
500
Over what interval is the function increasing? Over what interval is the function decreasing?
Increasing x<0.25
Decreasing x>0.25
500
The graph g is a translation 2 units right and 4 units up of the graph of f(x)=x2. Write function g in vertex form.
g(x)=(x-2)^2+4
500
Identify the vertex of the graph of this function:
f(x)=-x^2+4x+5
(2,9)
500
Janice wants to surround a 12 in. by 7in. painting with a frame that is w inches wide. Write a quadratic function A in standard form to represent the combined area A of the picture and the frame.
A(w)=4w^2+38w+84
500
Function f has constant first differences. Which of the following must be true?
A. The graph of f is a parabola.
B. The function f has constant values
C. The second differences for f are all zero.
D. The growth rate for f increases as x increases.
C. The second differences for f are all zero.