Question

The vertex of this parabola is at (2, -4). When the y-value is -1, the x-value is 3. What is the coefficient of the squared term in the parabola's equation?

Answer 1

`\bf ~~~~~~\textit{parabola vertex form} \\\\ \begin{array}{llll} \boxed{y=a(x- h)^2+ k}\\\\ x=a(y- k)^2+ h \end{array} \qquad\qquad vertex~~(\stackrel{2}{ h},\stackrel{-4}{ k})\\\\ -------------------------------\\\\ \underline{y}=a(\underline{x}-2)^2-4 \\\\\\ \textit{we also know that } \begin{cases} y=-1\\ x=3 \end{cases}\implies \underline{-1}=a(\underline{3}-2)^2-4 \\\\\\ 3=a(1)^2\implies 3=a`