Question

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.

Answer #1

solution:-

part d

part g

A ball is thrown into the air from an upstairs window and its
height, h, in feet t seconds after it is thrown is given by the
equation: h = –( t^2 – 8t – 20)
a. What is the maximum height that the ball reaches? You can
check your answer with a graphing utility, but first try to
determine your answer without the graph by rewriting the equation
in vertex form and using the information in the rewritten form....

For full credit be sure to show all work and units.
1. A 20 foot ladder leans against a vertical wall. The bottom of
the ladder slides away from the wall at 2 ft/sec.
a. How fast is the top of the ladder sliding down the wall when
the top of the ladder is 12 feet from the ground?
b. Interpret the meaning of the sign.
2. The current speed record for weight loss is 487 pounds to 130
pounds...

ch 6
1:
It is generally a good idea to gain an understanding of the
"size" of units. Consider the objects and calculate the kinetic
energy of each one.
A ladybug weighing 37.3 mg
flies by your head at 3.83 km/h
.
×10
J
A 7.15 kg
bowling ball slides (not rolls) down an alley at 17.5 km/h
.
J
A car weighing 1260 kg
moves at a speed of 49.5 km/h.
5:
The graph shows the ?-directed force
??...

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