Question 236860
Starting with the given function:
{{{h(t) = -16t^2+128t}}} you are being asked..."at what time, t, will h(t) = 240 ft."
So you set h(t) = 240 and solve for t.
{{{240 = -16t^2+128t}}} Subtract 240 from both sides and rearrange a bit.
{{{-16t^2+128t-240 = 0}}} Now you have a quadratic equation that can be solved by various methods.
I would factor -16 first just to simplify the calculations a bit.
{{{-16(t^2-8t+15) = 0}}} Notice the change of signs when we factored the -16!
Now, from the zero product rule, you get:
{{{t^2-8t+15 = 0}}} This can be solved by factoring.
{{{(t-3)(t-5) = 0}}} Apply the zero product rule again.
{{{t-3 = 0}}} or {{{t-5 = 0}}} so that...
{{{t = 3}}} or {{{t = 5}}}
Why are there two answers?
On the way up, the object will reach 240 feet in 3 seconds (t = 3).
On the way down, the object will again pass the 240-foot level in 5 seconds (t = 5).
Does this all make sense to you?