Acatapult launches a boulder with an upward velocity of 112 ft/s. the height of the boulder, h, in feet after t seconds is given by the function h = -16t2 + 112t + 30 how long does it take the boulder to reach its maximum height? what is the boulder’s maximum height? round to the nearest hundredth, if necessary

The expression for the height is given in quadratic expression form

Ax² + Bx + C

Where A, B, and C are constant

To find the x-coordinate when the graph reaches maximum/minimum, we use the formula

x = -B ÷ 2A

We have

h = -16t² + 112t + 30
The value for A = -16, B = 112, and C = 30

Substitute these into x = -B ÷ 2A we have
t = -112 ÷ (2×-16) = 3.5

The maximum height is reached when t = 3.5 sec 

The height when t = 3.5 sec is given
h = -16(3.5)² + 112(3.5) + 30 = 226 feet