Question 1071429
Standard Form Equation for a Parabola:
{{{y=a(x-h)^2+k}}}
for vertex (h,k)



What about the coefficient, a, in case you also have an included point on the parabola?


{{{a(x-h)^2=y-k}}}
{{{highlight_green(a=(y-k)/(x-h)^2)}}}-----and you would use your other given point to evaluate  a.  You were already also given (h,k) vertex.



Do you know what to do now?
( I did not substitute any values for you.)



--
Student wants further help:
Substituting the values, this happens.
{{{y=a(x+5)^2-1}}}
solving for a and substituting the other point's values,
{{{a=(3-(-3))/(-7-(-5))^2=1}}}
-
Standard Form equation is {{{y=(x+5)^2-1}}}.
Fully multiply and further arithmetic simplification gives you general form {{{y=x^2+10x+24}}}.