Afirecracker reaches a height of h feet before it bursts. the height h is modeled by h = −16t2 + vt + c, where v is the initial velocity, and c is the beginning height of the firecracker above the ground. the firecracker is placed on the roof of a building of height 15 feet and is fired at an initial velocity of 100 feet per second. will it reach a height of 100 feet before it bursts? identify the correct explanation for your answer.

General Idea:

If we have a quadratic function of the form f(x)=ax^{2} +bx+c , then the function will attain its maximum value only if a < 0 & its maximum value will be at x=-\frac{b}{2a} .

Applying the concept:

The height h is modeled by h = −16t^2 + vt + c, where v is the initial velocity, and c is the beginning height of the firecracker above the ground. The firecracker is placed on the roof of a building of height 15 feet and is fired at an initial velocity of 100 feet per second. Substituting 15 for c and 100 for v, we get the function as .

Comparing the function f(x)=ax^{2} +bx+c with the given function , we get , and .

The maximum height of the soccer ball will occur at t=\frac{-b}{2a}=\frac{-100}{2(-16)} = \frac{-100}{-32}=3.125 seconds

The maximum height is found by substituting in the function as below:

Conclusion:

Yes ! The firecracker reaches a height of 100 feet before it bursts.

no not all of them.

step-by-step explanation:

some of them have a square base.