A rock is thrown upward from a bridge that is 22 feet above a road. The rock reaches its maximum height above the road 0.69 seconds after it is thrown and contacts the road 2.53 seconds after it was thrown.

Write a function ff that determines the rock's height above the road (in feet) in terms of the number of seconds tt since the rock was thrown.

f(t)=.

Hint: the function ff can be written in the form f(t)=c⋅(t−t1)(t−t2)f(t)=c⋅(t-t1)(t- t2) for fixed numbers cc, t1t1, and t2t2.

Explanation:

The hint is that the function f can be written in the form:

It is a quadratic function, i.e. a parabola.

The maximum point, maximum height, of a parabola is its vertex.

And the x-coordinate of the vertex is at the midpoint between the two x-intercepts.

The time when the rock reaches the road is one x-intercept: t = 2.53 seconds: (2.53, 0).

The other x-intercept is sucht that (x + 2.53) / 2 = 0.69

Thus, the equation is:

You can find c by doing t = 0, because at t = 0 the height, f(t), is 22 feet:

Then, the function can be written as:

if the pizza is divided equally into 2 equal halves then you would get

πr^2/2

where r is the radius of the pizza.

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