Question

# 1. Ball Trajectory A child throws a ball from the window of a house. The height...

1. Ball Trajectory

A child throws a ball from the window of a house. The height of the ball, h(x), depends on the horizontal distance, x, from the window. Units are in feet. The function in expanded form is given by

h(?)= −4?2 +8?+5

a) Does this function have a mathematical domain restriction? Why or why not?

b) Factor the right side of the function (remember the GCF!).

c) Find the following function values: h(0), h(1), h (− 1) , h (5). Do not use a calculator. 22

Substitute into either the expanded or factored form, whichever is easier.

d) Using DESMOS, graph the function, and identify the coordinate points that correspond to the

function values in part c). Which of these 4 coordinate points are in the practical domain of the

function? Interpret their meaning.

e) State the practical domain and range of this function in interval notation.

f) On the practical domain, state the interval for x in which the height of the ball is decreasing.

g) Refer to your DESMOS graph and state the interval for x in which the ball is 7 feet or more

above the ground. To do this, add the line y = 7 to the function list and find the point of intersection to the nearest tenth.

solution:-

part d

part g