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The Pythagorean Proposition can help you explain this:
Answer: The function is .
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.
So, the function is maximum at x=35. Hence the vertex is (35,30)
The standard form of the parabola is,
Where (h,k) is vertex and a is scale factor.
Since vertex is (35,30).
The initial point is (10,2).
So the function of height is.
The graph of the function is shown below.
