quadratic word problem

Question

1. The distance in feet is modeled by the equation d = - 16x2 + 96x + 112 when a ball is tossed up in the air. To the nearest tenth of a second, how long will it take the ball to reach the ground? 

Answer 1

Answer 2

Athena,

Since this is a quadratic function, and x represents time, we are looking to see where this function would cross the x-axis if we were to graph it. This is where our our distance is zero. There are two times when the ball is zero (where the function crosses the x-axis/ not moving), when the ball is tossed and when it lands. We are looking for the zeros of this function. Again, we are looking for when our distance is zero, so the first thing we can do is plug in zero for d:

-16x^2 + 96x +112 = 0

Now we need to solve for x. There are many ways to do this. One way is by factoring:

1. Divide each term by -16 to make the coefficient of the quadratic term 1, since the coefficients of each term are divisible by -16
2. x^2 - 6x -7 = 0
3. Factor the trinomial (Factors of -7 that add to -6)
4. -7 and 1 add to give me -6 and multiply to -7, so our two factors are (x - 7)(x + 1)
5. Set each factor to zero to find the zeros (x-intercepts)
6. (x - 7) = 0 and (x + 1) = 0
7. Solve for x
8. x - 7 = 0 ---> add 7 to both sides, so x = 7
9. x + 1 = 0 ---> subtract 1 from both sides, so x = -1

Since x represents time, you cannot have negative time. Therefore, it takes the ball 7 seconds to reach the ground.

Hope this helps