79.0k views
2 votes
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

User Avalanchy
by
6.5k points

1 Answer

3 votes

Answer:

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.

User Siu
by
6.3k points