Algebra question

Question

An object is thrown upward at a speed of 172 feet per second by a machine from a height of 16 feet off the ground. The height h of the object after t seconds can be found using the equation h= -16t^2 + 172t + 16

When will the height be 432 feet?

When will the object reach the ground? 

Answer 1

For this type of problem, you simply have to plug in the values that are given to you, and then solve for the unknown variable.

In this case, we are given the height (h) of 432, so we can plug that into the equation to get

432 = -16t^2 + 172t + 16

Now we need to solve for the time (t), start by dividing both sides by 4

108 = -4t^2 + 43t + 4

4t^2 - 43t + 104 = 0 [move everything to one side]

You can use the quadratic formula to solve for t,

t = (1/8)(43 + √185)

For the second question, repeat the same steps, but instead of plugging in 432 for h, you will plug in 0, because the height is 0 when it hits the ground.