Question

a ball is thrown upward and outward from a height of 8 feet. the height of the ball, f(x), in feet, can be modeled by

\\f(x) = -0.4x^2 + 2.1x + 8\\

where x is the balls horizontal distance, in feet, from where it was thrown. use this model to solve parts (a) through (c).

a. what is the maximum height of the ball and how far from where it was thrown does this occur?

the maximum height is 10.8 feet, which occurs 2.6 feet from the point of release.
(round to the nearest tenth as needed.)

b. how far does the ball travel horizontally before hitting the ground?

7.8 feet
(round to the nearest tenth as needed.)

c. graph the function that models the balls parabolic path. choose the correct graph below.

Explanation:

Find the vertex of the quadratic model

Using the Maximum Value of Quadratic and Quadratic Word Problems knowledge points

$$
LATEXBLOCK0
$$

Find the horizontal distance when the ball hits the ground

Using the Quadratic Word Problems knowledge point

$$
LATEXBLOCK1
$$

Identify the correct graph of the function

Using the Parabola Graphing knowledge point

$$
LATEXBLOCK2
$$

Answer:

Question a

The maximum height is <blank>10.8</blank> feet, which occurs <blank>2.6</blank> feet from the point of release.

Question b

How far does the ball travel horizontally before hitting the ground?
<blank>7.8</blank> feet

Question c

• A. Graph with peak near y = 20 and x-intercept near x = 10
• B. Graph with peak near y = 10 and x-intercept near x = 20
• C. Graph with peak near y = 17 and x-intercept near x = 8
• D. Graph with peak near y = 11 and x-intercept near x = 7.8 (Correct answer)