Answer:
2344 feet is the max height
Step-by-step explanation:
<u>1) we find the function. </u>
<em>the function will be a parabola with a y intercept of 40. </em>
<em>the max height will be at the vertex. </em>
f(x) = ax^2 + bx + 40
<u>2) we find the derivative</u>
f'(x) = 2ax + b
<u>3) since the velocity is 96 at x = 0, we get the function: </u>
f'(x) = 2ax + 96
<u>4) find the x intercept of the velocity function</u>
0 = 2ax + 96
-96 = 2ax
-48/a = x
<em>This is the time in seconds when the max height is reached. </em>
<u>5) we finish the equation f(x)</u>
<em>since the antiderivative of 96 is 96x, we can write the equation: </em>
f(x) = -ax^2 + 96x + 40
<em>a will be negative since the parabola is opening downwards. </em>
<u>6) Since -48/a and -b/2a are both equal, a = 1</u>
f(x) = -x^2 + 96x + 40
<u>7) substitute 48 into x</u>
-48/a = 48
f(48) = -(48^2) + 96(48) + 40
f(48) = -2304 + 4608 + 40
f(48) = 2344
2344 feet is the max height