Question 889068
Complete the Square:
{{{f(x)=a(x^2+(5/(a2))x+6/a)}}}
{{{a(x^2+(5/(2a))x+(5/(4a))^2-(5/(4a))^2+6/a)}}}
{{{a((x+(5/(4a)))^2-(5/(4a))^2+6/a)}}}
{{{a(x+(5/(4a)))^2-a(5/(4a))^2+6}}}, almost finished standard form.


The extreme value happens when {{{x=-(5/(4a))}}} and {{{y=highlight_green(-a(5/(4a))^2+6=169/24)}}}; there you can solve for a.



{{{-a*(25/(16a^2))+6=169/24}}}
{{{-25/(16a)+6=169/24}}}
{{{6-25/(16a)=169/24}}}, LCD is 16*3a.
{{{6*16*3a-25*16*3a/(16a)=169*16*3a/24}}}
{{{6*16*3a-75=169*2*3a}}}
{{{169*6a-18*16a=-75}}}
{{{726a=-75}}}
{{{a=-75/726}}}
{{{a=-3*25/(242*3)}}}
{{{highlight(a=-25/242)}}}.