Question 327596
{{{f(x)=C(x+3)(x-2)}}}
where C is a constant to be determined using the maximum value of 25.
Move from this general form to the vertex form,
{{{f(x)/C=x^2-2x+3x-6}}}
{{{f(x)/C=x^2+x-6}}}
{{{f(x)/C=(x^2+x+1/4)-6-1/4}}}
{{{f(x)/C=(x+1/2)^2-25/4}}}
{{{f(x)=C(x+1/2)^2-(25C)/4}}}
The vertex of the equation is (-1/2,-25C/4) and the maximum occurs at the vertex.
For the maximum value equal to 25,
{{{-(25C)/4=25}}}
{{{C=-4}}}
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{{{f(x)=-4x^2-4x+24}}}
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{{{drawing(300,300,-5,5,-5,30,grid(1),circle(-3,0,.2),circle(2,0,.2),circle(-1/2,25,0.2),graph(300,300,-5,5,-5,30,-4x^2-4x+24))}}}