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.

a. turk and mcalister

b. howard, mission, and market

c. yes. since streets end some do not cross yet are not parallel to others. example: mcalister and 5th

step-by-step explanation:

parallel lines are lines which do not intersect ever and look a lot like railroad tracks. turk, mcalister and golden gate are examples of these.

intersect are streets which cross each other and a car on one can reach the other. howard, mission, and market intersect with 6th.

skew lines are lines which neither intersect nor are parallel. these lines exist here because some streets end and never intersect another like mcalister and 5th.