SKETCHING GRAPHS Sketch the graph of the function. Label the
coordinates of the vertex.
36. y 2x2
37. y 4x2
38. y x2 4x 1
39. y 4x2 8x 3
40. y x2 x 4
41. y 3x2 2x 1
42. y 2x2 5x – 3
43. y 4x2 4x 7
44. y 3x2 3x 4
EXAMPLE
Use a Quadratic Model
TABLE TENNIS The path of a
table-tennis ball that bounces
over the net can be modeled by
h 4.9x2 2.07x, where h is the
height above the table (in meters)
and x is the time (in seconds).
Estimate the maximum height
reached by the table-tennis ball.
Round to the nearest tenth.
Solution The maximum height of the table-tennis ball occurs at the vertex
of the parabolic path. Use a 4.9 and b 2.07 to find the x-coordinate of
the vertex. Round your solution to the nearest tenth.
b
2a
2.07
2(4.9)
≈ 0.2
Substitute 0.2 for x in the model and use a calculator to find the maximum
height.
h 4.9(0.2)2 2.07(0.2) 0.218 ≈ 0.2
ANSWER 䊳
45.
Nature
The maximum height of the table-tennis ball is about 0.2 meters.
You throw a basketball. The height of the ball can be
modeled by h 16t 2 15t 6, where h represents the height of
the basketball (in feet) and t represents time (in seconds). Find the vertex
of the graph of the function. Interpret the result to find the maximum
height that the basketball reaches.
BASKETBALL
DOLPHINS In Exercises 46 and 47,
use the following information.
DOLPHINS follow the path
INT
of a parabola when they jump
out of the water.
NE
ER T
More about dolphins
is available at
www.mcdougallittell.com
524
Chapter 9
46. What is the vertex of the
parabola? Interpret the result.
47. What horizontal distance did
the dolphin travel?
Quadratic Equations and Functions
Height (ft)
A bottle-nosed dolphin jumps out
of the water. The path the dolphin
travels can be modeled by
h 0.2d 2 2d, where h
represents the height of the dolphin
and d represents horizontal distance.
h
6
4
2
0
0
2
4
6
Distance (ft)
8
10
d