Question

A superhero is trying to leap over a tall building. The function f(x)=-16x^2+200x gives the superhero's height in feet as a function of time. The building is 612 feet high. Will the superhero make it over the building

Answer 1

Since
`\bigtriangleup \geq 0`, the superhero makes it over the building.

Explanation:

The height is given by the following function:

`f(x) = -16x^(2) + 200x`

Will the superhero make it over the building?

We have to find if there is values of x for which f(x) = 612.

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

`ax^(2) + bx + c, a\\eq0`.

This polynomial has roots
`x_(1), x_(2)` such that
`ax^(2) + bx + c = a(x - x_(1))*(x - x_(2))`, given by the following formulas:

`x_(1) = (-b + √(\bigtriangleup))/(2*a)`

`x_(2) = (-b - √(\bigtriangleup))/(2*a)`

`\bigtriangleup = b^(2) - 4ac`

If
`\bigtriangleup < 0`, the polynomial has no solutions.

In this question:

`f(x) = -16x^(2) + 200x`

`-16x^(2) + 200x = 612`

`16x^(2) - 200x + 612 = 0`

We have to find
`\bigtriangleup`

We have that
`a = 16, b = -200, c = 612`. So

`\bigtriangleup = (-200)^(2) - 4*16*612 = 832`

Since
`\bigtriangleup \geq 0`, the superhero makes it over the building.