Name _______________________________________ Date __________________ Class __________________
Practice B
Using Transformations to Graph Quadratic Functions
Graph the function by using a table.
1. f (x)  x2  2x  1
x
f (x)  x2  2x  1
(x, f (x))
2
1
0
1
2
Using the graph of f (x)  x2 as a guide, describe the transformations,
and then graph each function. Label each function on the graph.
2. h(x)  (x  2)2  2
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3. h(x)  (3x)2
_________________________________________
1 
4. h  x    x 
2 
2
_________________________________________
Use the description to write a quadratic function in vertex form.
5. The parent function f (x)  x2 is reflected across the x-axis, horizontally
stretched by a factor of 3 and translated 2 units down to create function g.
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6. A ball dropped from the top of tower A can be modeled by the function
h(t)  9.8t 2  400, where t is the time after it is dropped and h(t)is its
height at that time. A ball dropped from the top of tower B can be modeled
by the function h(t)  9.8t 2  200. What transformation describes this
change? What does this transformation mean?
________________________________________________________________________________________
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
Holt McDougal Algebra 2
Name _______________________________________ Date __________________ Class __________________
Practice B
Properties of Quadratic Functions in Standard Form
Identify the axis of symmetry for the graph of each function.
1. g(x)  x2  4x  2
________________________
2. h(x)  8x2  12x  11
________________________
3. k(x)  4(x  3)2  9
________________________
For each function, (a) determine whether the graph opens upward or
downward, (b) find the axis of symmetry, (c) find the vertex, and
(d) find the y-intercept. Then graph the function.
4. f(x)  x2  3x  1
a. Upward or downward
________________
b. Axis of symmetry
________________
c. Vertex
________________
d. y-intercept
________________
5. g(x)  2x2  4x  2
a. Upward or downward
________________
b. Axis of symmetry
________________
c. Vertex
________________
d. y-intercept
________________
Find the minimum or maximum value of each function. Then state the
domain and range of the function.
6. g(x)  x2  2x  1
7. h(x)  5x2  15x  3
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________________________________________
Solve.
8. A record label uses the following function to model the sales of a new release.
a(t)  90t 2  8100t
The number of albums sold is a function of time, t, in days. On which day
were the most albums sold? What is the maximum number of albums sold
on that day?
________________________________________________________________________________________
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
Holt McDougal Algebra 2