Question

Xavier shoots a basketball in which the height, in feet, is modeled by the equation,h(t) = -4t2 + 10 + 18, where t is time, in

seconds. What is the maximum height of the basketball?

Answer 1

The maximum height of the basketball is of 24.25 feet.

Explanation:

Vertex of a quadratic function:

Suppose we have a quadratic function in the following format:

`f(x) = ax^(2) + bx + c`

It's vertex is the point
`(x_(v), y_(v))`

In which

`x_(v) = -(b)/(2a)`

`y_(v) = -(\Delta)/(4a)`

Where

`\Delta = b^2-4ac`

If a<0, the vertex is a maximum point, that is, the maximum value happens at
`x_(v)`, and it's value is
`y_(v)`.

Height of the basketball:

Given by the following function:

`h(t) = -4t^2 + 10t + 18`

Which is a quadratic function with
`a = -4, b = 10, c = 18`

What is the maximum height of the basketball?

y(in this case h) of the vertex. So

`\Delta = b^2-4ac = 10^2 - 4(-4)(18) = 388`

`y_(v) = -(388)/(4(-4)) = 24.25`

The maximum height of the basketball is of 24.25 feet.