Answer:

toy rocket is fired into the air from the top of a barn. Its height (h)" role="presentation" style="display: inline-flex; font-style: normal; font-weight: normal; line-height: normal; font-size: 18px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: 100%; max-height: none; min-width: 0px !important; min-height: 0px; border: 0px; padding: 0px; margin: -2px 0px 0px; overflow: auto hidden; vertical-align: middle; position: relative;">(h)(h) above the ground in yards after t" role="presentation" style="display: inline-flex; font-style: normal; font-weight: normal; line-height: normal; font-size: 18px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: 100%; max-height: none; min-width: 0px !important; min-height: 0px; border: 0px; padding: 0px; margin: -2px 0px 0px; overflow: auto hidden; vertical-align: middle; position: relative;">tt seconds is given by the function h(t)=−5t2+10t+20" role="presentation" style="display: inline-flex; font-style: normal; font-weight: normal; line-height: normal; font-size: 18px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: 100%; max-height: none; min-width: 0px !important; min-height: 0px; border: 0px; padding: 0px; margin: -2px 0px 0px; overflow: auto hidden; vertical-align: middle; position: relative;">h(t)=−5t2+10t+20h(t)=−5t2+10t+20.

What was the maximum height of the rocket?How long was the rocket in the air before hitting the ground?At what time(s) will the rocket be at a height of 22 yd?Applications of Quadratic Functions

There are many real-world situations that deal with quadratics and parabolas. Throwing a ball, shooting a cannon, diving from a platform and hitting a golf ball are all examples of situations that can be modeled by quadratic functions.

In many of these situations you will want to know the highest or lowest point of the parabola, which is known as the vertex. For example, consider that when you throw a football, the path it takes through the air is a parabola. Natural questions to ask are:

"When does the football reach its maximum height?""How high does the football get?"

If you know the equation for the function that models the situation, you can find the vertex. If the function is f(x)=ax2+bx+c" role="presentation" style="display: inline-flex; font-style: normal; font-weight: normal; line-height: normal; font-size: 18px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: 100%; max-height: none; min-width: 0px !important; min-height: 0px; border: 0px; padding: 0px; margin: -2px 0px 0px; overflow: auto hidden; vertical-align: middle; position: relative;">f(x)=ax2+bx+cf(x)=ax2+bx+c, the x-coordinate of the vertex will be −b2a" role="presentation" style="display: inline-flex; font-style: normal; font-weight: normal; line-height: normal; font-size: 18px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: 100%; max-height: none; min-width: 0px !important; min-height: 0px; border: 0px; padding: 0px; margin: -2px 0px 0px; overflow: auto hidden; vertical-align: middle; position: relative;">−b2a−b2a. The y-coordinate of the vertex can be found by substituting the x-coordinate into the function. In the case of the football:

The x-coordinate of the vertex will give you the time when the football is at its maximum height.The y-coordinate will give you the maximum height.

One way to understand where the −b2a" role="presentation" style="display: inline-flex; font-style: normal; font-weight: normal; line-height: normal; font-size: 18px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: 100%; max-height: none; min-width: 0px !important; min-height: 0px; border: 0px; padding: 0px; margin: -2px 0px 0px;