SOLUTION: Karen is throwing an orange to her brother Saul, who is standing on the balcony of their home. The height, h (in feet), of the orange above the ground t seconds after it is thrown

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Question 1072260: Karen is throwing an orange to her brother Saul, who is standing on the balcony of their home. The height, h (in feet), of the orange above the ground t seconds after it is thrown is given by: h (t)=-16t^2+32t+4
If Saul's outstretched arms are 18 feet above the ground, will the orange ever be high enough that he can catch it?
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!

We need the maximum value of a quadratic function.

The maximum value of a quadratic function 

f(x) = ax^2 + bx + c

with a negative leading coefficient, is when the value of x
equals -b%2F%282a%29

In this problem x is t and f is h, a is -16 and b is +32
c is 4 but we don't need it to find the time t when the
function h(x) (for height) has its maximum value.

h(t)=-16t^2+32t+4

-b%2F%282a%29=-expr%28%22%22+%2B+32%29%2F%282%28-16%29%29=%28-32%29%2F%28-32%29=1

So it reaches the maximum height in 1 second.  So we
substitute 1 for t in the equation

h(1) = -16(1)^2+32(1)+4 = -16+32+4 = 20 feet.

So yes, that's high enough for him to catch the orange.

Edwin