Question

The vertex of this parabola is at (4, -3). when the x-value is 5, the y-value is -6. what is the coefficient of the squared expression in the parabola's equation?
*sorry edited now 

Answer 1

$\bf y=a(x-\boxed{h})^2+\boxed{k}\qquad vertex\ (h,k) \\ \quad \\ \textit{we know the vertex is at 4,-3}\implies \begin{array}{lrlll} 4&-3\\ h&k \end{array} \\ \quad \\ y=a(x-h)^2+k\\\\ y=a(x-(4))^2+(-3)\implies y=a(x-4)^2-3 \\ \quad \\ \textit{we also know that} \begin{cases} x=5\\ y=-6 \end{cases}\textit{ so, what is the coefficient "a"?} \\ \quad \\ \boxed{-6}=a(\boxed{5}-4)^2-3\impliedby \textit{solve for "a"}$