Question

6. A football punt at a Kansas City Chiefs game reaches a maximum height
of 44 feet after traveling a horizontal distance of 9 feet. Assume the ball is
kicked from (0,0). Draw and label a picture of a quadratic that represents
the situation.*

Answer 1

The quadratic equation that represents the situation is y = -44/81(x - 9)^2 + 44

How to determine the quadratic equation?

The maximum is at:

Height of 44 feet at an horizontal distance of 9 feet.

This represents the vertex.

i.e.

(h, k) = (9, 44)

A quadratic function is represented as:

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

So, we have:

y = a(x - 9)^2 + 44

The ball is kicked from (0,0)

This means that

(x, y) = (0,0)

So, we have:

0 = a(0 - 9)^2 + 44

Evaluate

0 = 81a + 44

This gives

81a = -44

Divide by 81

a = -44/81

Substitute a = -44/81 in y = a(x - 9)^2 + 44

y = -44/81(x - 9)^2 + 44

Hence, the quadratic equation that represents the situation is y = -44/81(x - 9)^2 + 44

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