Question 115511
a)

Remember, if an equation is in vertex form {{{y=(x-h)^2+k}}}, then we know the vertex is (h,k)

Since we can see that the vertex is (-6,0), this means h=-6 and k=0


{{{y=(x-h)^2+k}}} Start with the general equation in vertex form. In this case, a=1


{{{y=(x-(-6))^2+0}}} Plug in h=-6 and k=0.



{{{y=(x+6)^2+0}}} Rewrite {{{x-(-6)}}} as {{{x+6}}}.



{{{y=(x+6)^2}}} Remove the zero term.



So the equation of the parabola that has been shifted 6 units to the left is {{{y=(x+6)^2}}}