Vocabulary
The line that divides the parabola into two matching halves
axis of symmetry
Find the axis of symmetry using -b/2a
f(x)=-9x2+1
x=0
How does the graph of f(x) = x2+2 compare to the graph of g(x) = x2+8 (name the transformation(s))
The graph of g(x) is the graph of f(x) shifted 6 units up.
The y-values increase to a maximum, then decrease, or decrease to a minimum, then increase
Quadratic Function
h(x) = 1/5 x2
Evaluate h(20)
h(20) = 80
The name of the shape of a quadratic on a graph
Parabola
What is the y-intercept of the following quadratic:
f(x) = 2x2+4x-6
y-intercept = (0,-6)
What is the vertex of the graph (x+8)2-3?
(-8,-3)
If this were a TABLE of x and y values, what type of function would it represent?
x -2 -1 0 1 2
y -14 -2 2 -2 -14
Quadratic
What is the function in standard form?
f(x) = -2(x-9)2+15
f(x) = -2x2+36x-147
F(x) = x2
Quadratic Parent Function
Find the axis of symmetry using -b/2a
f(x)=4x2+24X+131
x = -3
What is the axis of symmetry of the function
f(x) = -(x+1)2+2
axis of symmetry: x = -1
The percent of growth or decay is constant
Exponential Function
Solve.
f(x) = 2x2+24x+64.
Let x = 12
f(12) = 640
The lowest or highest point on the graph of a quadratic function
Vertex
Write the following quadratic in standard form
f(x)=(x-2)(x+1)
f(x)= x2-x-2
How does the value of a, h, and/or k affect the vertex for the graph of the function j(x) = −1/2x2 + 8 compared to the parent function f(x) = x2?
It opens downward, is wider, and is translated up 8 units
The rate of change is constant
Linear Function
Cindy's square garden has a side length of x feet. She will plant 5 tulip bulbs per square foot. The function g(x) = 5x2 models the number of bulbs she will plant. How many bulbs will she plant if the garden has a side length of 8 feet?
320 bulbs
The formula to find the axis of symmetry
-b/2a
f(x)=-2(x-1)2+7 is a quadratic in vertex form. Change it to standard form.
f(x) = -2x2+4x+5
How does the graph f(x) = -3(x-5)2+7 compare to the graph of the parent function?
It opens downward and narrower, moves right 5 spaces, and up 7 spaces.
If this were a TABLE of x and y values, what type of function would it represent?
x 2 4 6 8 10
y 3 9 27 81 243
Exponential function
What function models the area of a rectangle with side lengths 2x-4 units and x+1 units?
100 BONUS POINTS: What is the area when x=3?
f(x)=2x2-2x-4
A=8