Question 1074355
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<pre>
An equation for the height as a function of time is

h(t) = -16t^2 + 128t.

To answer the question, you should solve an inequality


h(t) > 128,   or   -16t^2 + 128t > 128.


It is equivalent to 16t^2 - 128t + 128 < 0,  or  t^2 -8t + 8 < 0.


To solve it, solve the quadratic equation t^2 -8t + 8 = 0.


{{{t[1,2]}}} = {{{(8 +- sqrt(64-4*8)))/2}}} = {{{(8 +- sqrt(32))/2}}} = {{{4 +- 2*sqrt(2)}}}.


Now the answer is:  at {{{4 -2*sqrt(2)}}} < t < {{{4 + 2*sqrt(2)}}} seconds the projectile's height exceeds 128 feet.
</pre>


{{{graph( 330, 330, -1.5, 8.5, -10.5, 140.5,
          -16x^2 + 128x - 128
)}}}


Plot y = {{{-16x^2 + 128x - 128}}}