Question 225879
{{{y=ax^2+k}}} Start with the given equation.



{{{0=a(2)^2+k}}} Plug in {{{x=2}}} and {{{y=0}}} from the given point (2,0)



{{{0=4a+k}}} Square 2 to get 4.



{{{-4a=k}}} Subtract 4a from both sides.



So {{{k=-4a}}}



-----------------



{{{y=ax^2+k}}} Go back to the given equation.



{{{-6=a(4)^2+k}}} Plug in {{{x=4}}} and {{{y=-6}}} from the given point (4,-6)



{{{-6=16a+k}}} Square 4 to get 16.



{{{-6=16a-4a}}} Plug in {{{k=-4a}}}



From here, solve for 'a'. Once you have the value of 'a', plug it into {{{k=-4a}}} to find 'k'.