Question

Texas University Quarterback, Michael Daniels, is standing on his own 10-yard line. He throws a pass tword 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 downfeild at a point 2 yards above the ground. Let X be the number of yards the football travels horizontally, and let Y be the number of yards the ball is above ground.
Draw the graph of the function

Answer 1

Answer: The function is $y=-\frac{28}{625}(x-35)^2+30$.

Explanation:

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.