Question 120926
First, notice that x-intercepts in a quadratic function are easily identified when we set the function =0. After factoring such a function, we will get something resembling:{{{(x-a)(x-b)=0}}}. That equation, to be true, must have either factor =0. That is, {{{x-a=0}}} or {{{x-b=0}}}. Then, the x-intercepts are a and b because they satisfy each equation.

You should now be able to see that we are looking for a modified version of the following equation: {{{(x-3)(x-7)=0}}}. When we expand this, we get {{{x^2-10x+21=0}}}. Let the left side be our {{{f(x)}}}.

Then, {{{f(x)=x^2-10x+21}}}. If we take {{{f(5)=5^2-10(5)+21=25-50+24=-4}}}. Then, what should we multiply -4 by to get an answer of 8? {{{-4a=8}}} implies {{{a=-2}}}. Now, multiply the right side of the {{{f(x)}}} we found by this {{{a=-2}}}, to form a new function {{{g(x)}}}:

{{{g(x)=-2(x^2-10x+21)}}}

Check:
{{{g(5)=-2(25-50+21)=-2*-4=8}}} 

Note that {{{g(x)=-2 f(x)}}}, AND the zeros remain unchanged. For a simple graphical example, look at the following:

{{{graph(300,200,-1,10,-5,6,x^2-10x+21,-2(x^2-10x+21))}}}