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.

goog may have it for you

when rotating a figure 180 degrees, imagine that you are able to take the figure and turn it clockwise or counterclockwise around a center point. to rotate a figure 180 degrees, you will need to apply the rule (x, y) → (-x, -y). start by using a coordinate grid with coordinates for each vertex of the figure. the center point of the coordinate grid is located at (0, 0), which is what you will rotate the figure around. write down the original coordinates of the shape you are going to rotate. then, apply the rule. for example, coordinate (1, 2) becomes (-1, -2). another example would be, coordinate (-4, -2) becoming (4, 2). after you change each original coordinate to the rotated coordinate, you will draw your new figure.

step-by-step explanation: