Quadratic Function CHARACTERISTICS
Quadratic Function TRANSFORMATIONS
Exponential Functions
Variables / Factoring
Exponents / Square Roots
100
What is the y-intercept(s) of the function?
(0, -3)
100
The graph of f(x) = x2 was transformed to create the graph of g(x) = f(x) - 1234.
Describe the transformation(s) from the graph of f to the graph of g?
Vertical shift down 1234
100
The function, y=527(1.03)x, defines the relationship between years and gallons of water collected.
What is the initial value of gallons of water? How do you know?
527 gallons of water because the "a" represents initial/start value.
100
Simplify the expression, (3ak - 10kz + 4wz) + (4ak - 2kz - 6wz)
4ak - 12kz -2wz
100
Simplify the expression, √18. Show your work.
3 √2
200
What is the axis of symmetry for the function?
x = -1
200
The graph of f(x) = x2 was transformed to create the graph of g(x) = f(x - 77) + 83.
Describe the transformation(s) from the graph of f to the graph of g?
Horizontal shift of 77 to the right
Vertical shift of up 83
200
The function, y=527(1.03)x, defines the relationship between years and gallons of water collected.
Is the amount of water increasing or decreasing? How do you know?
Increasing because the "b" is greater than 1
200
Simplify the function, y = 2 (6x - 1)2 -5
y = 72x2 - 24x -3
200
Simplify (a4 b3 c)2
a8 b6 c2
300
Does the function have a maximum or minimum? And what is the value of it?
Minimum of -4
300
The graph of f(x) = x2 was transformed to create the graph of g(x) = -9/27 f(x).
Describe the transformation(s) from the graph of f to the graph of g?
Reflection over the x-axis
Vertical compression of 9/27
300
How do you know?The function, y=527(1.03)x, defines the relationship between years and gallons of water collected.
What is the rate, as a percent, for gallons of water per year? Show your work.
3%
300
What two factors create an expression equivalent to 4x2 - 81?
(2x - 9)(2x + 9)
300
Simplify the expression, 2 √98. Show your work.
14 √2
400
What are the zeros of the function?
(-3, 0) , (1, 0)
400
Write a function, g(x), that transforms f(x) = x2 to reflect over the x-axis, compress vertically by 2/7, shift to the left 23, and shift down 8.
g(x) = - 2/7 (x + 23)2 - 8
400
A sample of a substance with an initial mass of 583 grams is decaying at a rate of 27% per hour.
Create a function that can be used to find y, the mass of the substance in grams remaining after x hours.
y = 583(0.73)x
400
What are the factors of 2x2 + 11x + 12? Show your work.
(x + 4)(2x + 3)
400
Simplify ( a8 b6 c2 )( a7 b9 c13 )
a15 b15 c15
500
What is the domain and range for the following graph?
Domain: All Real Numbers
Range: x ≥ -4
500
The graph of f(x) = x2 was transformed to create the graph of g(x) = -9 (x + 7)2 + 4.
Describe the transformation(s) from the graph of f to the graph of g?
Reflection over x-axis
Vertical stretch of 9
Horizontal shift of 7 to the left
Vertical shift of 4 up
500
A beehive currently has 500 bees. The number of bees is expected to grow at a rate of 24% each year.
Create an exponential function to model the number of bees in the beehive, y, after x, years.
y = 500 (1.24)x
500
What are the factors of 4x2 - 15x + 9? Show your work.
(4x - 3)(x - 3)
500
Simplify ( a12 (b8)4 ) / ( a6 )
a6 b32