Question

The height h (in feet) of an object t seconds after it is dropped can be modeled by the quadratic equation
h = -16t2 + h0, where h0 is the initial height of the object. Suppose a small rock dislodges from a ledge that is 255 ft above a canyon floor. Solve the equation h = -16t2 + 255 for t, using the quadratic formula to determine the time it takes the rock to reach the canyon floor.

Answer 1

Starting with h = -16t^2 + 255

at the canyon floor, h = 0

So h = -16t^2 + 255
Becomes

0 = -16t^2 + 255

Solve for t. You don’t actually need the quadratic formula, but because it specifically asks for it: ax^2 + bx + c = 0 is the generic form of a quadratic equation. In this case, a = -16, b = 0, and c = 255. In place of x, use t since that’s the variable in our height equation.

Plug a b and c into the quadratic formula and solve for t.