Question 1125614
.
<pre>
They want you find the minimum of this quadratic function


    f(x) = {{{x^2}}} + {{{(18-4x)^2}}} = {{{x^2 + 324 - 144x + 16x^2}}} = {{{17x^2 - 144x + 324}}}.


For the general form of a quadratic function  y = ax^2 + bx + c  the minimum is achieved at  x = {{{-b/(2a)}}}.


In your case the minimum is at  x= {{{- (-144)/(2*17)}}} = {{{72/17}}}.


The pair under the question is  x = {{{72/17}}},  y = {{{18 - 4*(72/17)}}} = {{{18/17}}}.
</pre>

Solved.