Question

1. A ball is thrown off of a balcony and it's height can be

modeled using the function, f(x) = -x2 + 4x + 12, where x is
the number of second after the ball was released. After
how many seconds will it the ball to hit the ground?

Answer 1

After 6 seconds, the ball will hit the ground.

Explanation:

f(x)=-x^2 + 4x + 12

Since we want to see when it touches the ground, the height must be equal to 0, so f(x) has to equal 0.

0=-x^2 + 4x + 12

If you factor this equation, you'd get:

(-x + 6)(x + 2) = 0

We get the 2 and the 6 from the factors of 12. The two factors of 12 have to be able to add or subtract into 4, and in this case, 6-2 is 4. (If you multiply this equation out, you'd get the same one you started with)

Since we need it to equal 0, the way to multiple to 0 is to have a zero itself. This means that either (-x+6) is equal to 0 or (x+2) is equal to 0. The only x values that satisfy this is 6 and -2. You can't have -2 seconds after, so it has to be 6.

Hope that helps.