Question 22916
So, you want to solve the equation;


{{{f(x) = x^2 + 6x + 5}}} 

and then graph it....

Well first set it up

{{{0 = x^2 + 6x + 5}}}

And then factor....you have to ask yourself...what two factors of 5 add up to six? Well, there are ONLY two factors of 5, that is 1 and 5 (because 1 * 5 = 5). So, go ahead and factor;

{{{0 = (x+1)(x+5)}}}

***If you foil that, you'll get back to the original equation

Now use something called the zero product property, which means set the equations inside of those parentheses to zero, and solve;

{{{x+1 = 0}}}   & {{{x+5 = 0}}}
{{{x = -1}}}    & {{{x = -5}}}

Those are the solutions...

Now, to find the vertex, use the formula;

{{{x = (-b/2a)}}}

So, we are going to plug in the values of the a, b and c from the orignal equation. Remember {{{ ax^2 + bx + c }}}

{{{ x = (-6/2(1)) }}}
{{{ x = -3 }}}


Now, finally, here is the graph...


{{{graph(300,200,-7,3,-5,10,x^2+6x+5)}}}