Question

The vertex of this parabola is at (-4, -1). When the y-value is 0, the x-value is 2. What is the coefficient of the squared term in the parabola's equation?

Answer 1

$\bf \qquad \textit{parabola vertex form}\\\\ \begin{array}{llll} \boxed{y=a(x-{{ h}})^2+{{ k}}}\\\\ x=a(y-{{ k}})^2+{{ h}} \end{array} \qquad\qquad vertex\ ({{ h}},{{ k}})\\\\ -------------------------------\\\\ y=a(x-(-4))^2-1\implies y=a(x+4)^2-1 \\\\\\ \textit{now, we also know that } \begin{cases} y=0\\ x=2 \end{cases}\implies \underline{0}=a(\underline{2}+4)^2-1$

solve for "a"