Question 1098543
.
<pre>
They instruct you that your formula is

h(x) = {{{-((32*x^2)/150^2) + x}}}.


I forget about this "graphing utility" which is mentioned in the text, since I don't know what is they are talking about,
and, probably, I do not have it at all (thanks to god).


I will show you how to calculate it directly by hand.

Simply substitute the value of 80 into the formula and calculate:

h(x) = 80 = {{{-((32*x^2)/150^2) + x}}}.


Now you need to find x from this equation

80 = {{{-((32*x^2)/150^2) + x}}}.


For it, multiply both sides by 150^2 = 22500. You will get

80*22500 = -32x^2 + 22500x,   or,  equivalently,

32x^2 - 22500x  + 1800000 = 0.


Apply the quadratic formula

{{{x[1,2]}}} = {{{(22500 +- sqrt (22500^2 - 4*32*1800000))/(2*32)}}} = {{{(22500 +- 16609)/64}}}.

{{{x[1]}}} = {{{(22500 - 16609)/64}}} = 92;

{{{x[2]}}} = {{{(22500 + 16609)/64}}} = 611.


<U>Answer</U>.  There are two solutions:  92 ft  and  611 ft  (approximately).
</pre>


{{{graph( 800, 200, -50.5, 750.5, -20.5, 180.5,
          -((32*x^2)/150^2) + x, 80
)}}}


Plot y = {{{-((32*x^2)/150^2) + x}}} (red) and y = 80 (green)