Question

The vertex of this parabola is at (-5, -2). When the x-value is -4, the y-value is 2. What is the coefficient of the squared expression in the parabola's equation?

Answer 1

`\bf \qquad \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\ ({{ h}},{{ k}})\\\\ -----------------------------\\\\ \textit{vertex at -5,-2}\quad \begin{cases} h=-5\\ k=-2\\ \end{cases}\implies y=a(x-(-5))^2+(-2) \\\\\\ y=a(x+5)^2-2\quad \begin{cases} x=-4\\ y=2 \end{cases}\implies \underline{2}=a(\underline{-4}+5)^2-2 \\\\\\ 2=a(1)^2-2\implies \boxed{4=a}`