Question 968373
(a):


Factorize the right-hand member and you have the factored form.
{{{y=(x+5)(x+7)}}};
You also see directly from this that the roots are  -5 and -7.


(b):


Complete the Square for the quadratic right-hand expression.  See your textbook's lesson on this or study the lesson available here:  <a href="http://www.algebra.com/my/Completing-the-Square-to-Solve-General-Quadratic-Equation.lesson?content_action=show_dev">http://www.algebra.com/my/Completing-the-Square-to-Solve-General-Quadratic-Equation.lesson?content_action=show_dev</a>.


Your term to use is {{{(12/2)^2=6^2}}}.


{{{x^2+12x+35}}}
{{{x^2+12x+6^2+35-6^2}}}
{{{(x+6)^2+35-36}}}
{{{highlight(y=(x+6)^2-1)}}}


You can compare how the two forms of equation appear.  The standard form, found after completing the square, lets you read the vertex directly from the equation.  Vertex is a minimum, at (-6,-1).


Graph the equation?
You have the vertex, you know it is a minimum, and you have the two roots.  You can graph this.