It is given that Michael Daniels, is standing on his own 10-yard line. He throws a pass toward the opposite goal line. The football is 2 yards above the ground when the quarterback lets it go.

It follows a parabolic path. Reaching its highest point, 30 yards above the ground. It is caught 50 yards downfield at a point 2 yards above the ground.

So, the initial point is (10,2) and the other point is (60,2).

The height function of a football represents a downward parabola. The maximum point of the function is called vertex. So the vertex is (h,30).

The two point (10,2) and (60,2) have same y-coordinate, therefore the function is maximum at the midpoint of both points.

$midpoint=(\frac{10+60}{2}, \frac{2+2}{2})=(35,2)$

So, the function is maximum at x=35. Hence the vertex is (35,30)

The standard form of the parabola is,

$y=a(x-h)^2+k$

Where (h,k) is vertex and a is scale factor.

Since vertex is (35,30).

$y=a(x-35)^2+30$

The initial point is (10,2).

$2=a(10-35)^2+30$

$-28=625a$

$a=-\frac{28}{625}$

So the function of height is.

$y=-\frac{28}{625}(x-35)^2+30$

The graph of the function is shown below.

3 0

3 years ago

A water tank with 265 gallons of water has a leak. After 5 hours, the tank is completely empty.

ddd [48]

<span>The water tank loses 53 gallons of water in 1 hour.</span>

3 0

3 years ago

Read 2 more answers

Find the distance that the earth travels in eight days in its path around the sun. assume that a year has 365 days and that the

lora16 [44]

The speed of earth will be found as follows:
speed=distance/time
distance=93 million
time=365
speed=(93)/365=254, 794.5205 mi/day
thus distance moved for 8 days will be:
distance=speed*time
=(254794.5205)×8
=2,038,356.164 miles

5 0

4 years ago