Question 742539
Use standard form equation to fill-in the vertex information from your given (h, k).  {{{y=a*(x+3)^2-14}}}, and we know before continuing that {{{a>0}}}, as we can find inspecting the vertex and the y intercept.


Substitute the y-intercept coordinate values into the equation and solve for a.
{{{13=a(0+3)^2-14}}}
{{{13+14=9*a}}}
{{{27=9*a}}}
{{{a=3}}}


Equation for this parabola is {{{highlight(y=3(x+3)^2-14)}}}.


Finding the x-intercepts requires just setting y=0 and solve for x from the standard form equation just found:
{{{3(x+3)^3-14=0}}}
{{{3(x+3)^3=14}}}
{{{(x+3)^2=14/3}}}
{{{x+3=0+- sqrt(14/3)}}}
{{{highlight(x=-3+- sqrt(14/3))}}}, the x-intercepts.