Name _______________________________________ Date __________________ Class __________________
Unit 2
Practice Test
1.
Can two different quadratic functions
have the same zeroes? Explain. Draw a
picture to show your solution.
2.
How many solutions can a quadratic
function have? What are the other
names for the solutions of a quadratic
function?
3.
Graph the axis of symmetry, the vertex,
the point containing the y-intercept, and
another point. Then reflect the points
across the axis of symmetry. Connect the
points with a smooth curve.
Graph the function to determine
approximately how long it takes the ball
to hit the ground.
9. Graph y  x2  3
10. Solve each equation by graphing a
related function.
a.) y  (x  1)(x – 3)
4.
1
b.) y  ( x  8)( x  2)
2
What are the x-intercepts of y  4 x 2  16 ?
5.
Write each function in standard form:
a.) 0  (x 5)2  2
b.) 1/2(x  1)2 – 2 = 0
c.) (x 5)2 – 4 = 0
11. What are the zeros of a function?
a.) y  2(x  1)(x + 3)
12. A shark jumps out of water. The function
h(t) = -16t 2 +18t models the height, in
feet, of the shark above water after t
seconds. How long is the shark out of
the water? What is the maximum height
of the shark above the water?
b.) y  1/3(x 2)  9
2
c.) y  -4(x  5)(x + 7)
6.
Graph each quadratic function, then
identify the x-intercepts and the axis of
symmetry of each graph each quadratic
function and each parabola.
13. A fish jumps out of water. The function
h(t) = -16t 2 +11t models the height, in
feet, of the fish above water after t
seconds. How long is the fish out of
water? What is the maximum height of
the fish above the water?
a.) y  (x  1)(x + 3)
b.) y  -2(x  1)(x – 5)
c.) y  (2x  5)(2x + 7)
7.
8.
The zeros of a quadratic function are
( 1, 0) & (3, 0) . What is a possible vertex
of the function?
A (1, 0)
C (2, 0)
B (1,  2)
D (2,  2)
14. A bird is in a tree 30 feet off the ground &
drops a twig that lands on a bush 25 feet
below. The function h(t) = -16t2 + 30,
where t represents the time in seconds, h
gives the height, in feet, of the twig above
the ground as it falls. When will the twig
land on the bush?
A tennis ball is tossed upward from a
balcony. The height of the ball in feet can
be modeled by the function y = -4(2x + 1)
(2x - 3) where x is the time in seconds
after the ball is released. Find the
maximum height of the ball and the time
it takes the ball to reach this height.
15. What would the factored form of a
quadratic look like if there were only one
x–intercept?
16. What is the domain and range of the
function, y = -8(x 5)2 – 2?
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
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Name _______________________________________ Date __________________ Class __________________
Unit 2
Practice Test
f) x  3  x2  3
17. Complete the following for the parabola
f(x)  2(x  3)2  4.
23. Solve by factoring
The vertex is _______. The graph
opens ___________. The function has a
minimum value of _______
a) 2x2  32  0
b) 3x2  7x  x  4
18. The graph below is a translation of y = x2
c) 2x2  7  14  11x
a.) What is the horizontal translation?
d) 5x2  20x  20  0
e) 5x2  6x  5x  2
b.) What is the vertical translation?
f) 2x(3x  10)  2x2  25
c.) What is the equation of the graph?
g) 2(x3)(x  3)  14
24. Solve by factoring (special factors)
a) 4x2  20x  25 = 0
b) 25x2  30x  9 = 0
c) 36x2  16 = 0
d) 49x2  14x  1  0
19. Graph the following parabolas.
a.) y  (x 5)2  2
25. Factor using special factors
b.) y  -2(x  1)2  2
a) x2  10xy  25y2
c.) y  1/2(x 2)2  3
b) 81x2  121y2
c) 75x3  48x
20. A group of friends tries to keep a small
beanbag from touching the ground by
kicking it. On one kick, the beanbag’s
height can be modeled by the equation h
= -2(t – 1) -16t(t – 1), where h is the
height of the beanbag in feet and t is the
time in seconds. Find the time it takes the
beanbag to reach the ground.
d) 32x2  80xy  50y2
26. The area of a room is 396 ft2. The length
is (x + 3) feet, & the width is (x + 7) feet.
Find the dimensions of the room.
27. A ball is dropped from a height of 64 feet.
Its height, in feet, can be modeled by the
function h(t) 16t 2 64, where t is the
time in seconds since the ball was
dropped. After how many seconds will
the ball hit the ground?
21. Find the zeros of each function.
a.) f(x)  (x  1)(x  1)
b.) f(x)  (4x  7)(x  2)
c.) f(x)  x(x  4)  2(x  4)
28. A model rocket fired from the ground at
time t can be modeled by the equation h
= -490t2 + 1120t. When is the height of
the model rocket 640 centimeters?
d.) f(x)  3x(x  7)  7(x  7)
e.) f(x)  -3x(x  9)
22. Solve by factoring.
29. A projectile is launched from an
underground silo 81 feet deep. Its height
follows the equation h  16t2  72t  81.
When does the projectile land back on
the ground?
a) x  25  0
2
b) x2  2x  1  0
c) x2  5x  4  0
d) x2  3x  11  43
e) x2  8x  63  8x
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
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