Answer: The function is [tex]y=-\frac{28}{625}(x-35)^2+30[/tex].
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.
[tex]midpoint=(\frac{10+60}{2}, \frac{2+2}{2})=(35,2)[/tex]
So, the function is maximum at x=35. Hence the vertex is (35,30)
The standard form of the parabola is,
[tex]y=a(x-h)^2+k[/tex]
Where (h,k) is vertex and a is scale factor.
Since vertex is (35,30).
[tex]y=a(x-35)^2+30[/tex]
The initial point is (10,2).
[tex]2=a(10-35)^2+30[/tex]
[tex]-28=625a[/tex]
[tex]a=-\frac{28}{625}[/tex]
So the function of height is.
[tex]y=-\frac{28}{625}(x-35)^2+30[/tex]
The graph of the function is shown below.
