Question

If the vertex of a parabola is (-4, 6) and another point on the curve is (-3, 14), what is the coefficient of the squared expression in the parabola's equation?

Answer 1

$\bf \qquad \textit{parabola vertex form}\\\\\begin{array}{llll} \boxed{y=a(x-{{ h}})^2+{{ k}}}\\\\ x=a(y-{{ k}})^2+{{ h}} \end{array}\qquad\qquad vertex\ ({{ h}},{{ k}})\\\\ -------------------------------\\\\ vertex\ (-4,6)\qquad \begin{cases} h=-4\\ k=6 \end{cases}\implies y=a(x-(-4))^2+6 \\\\\\ y=a(x+4)^2+6 \\\\\\ \textit{we also know that } \begin{cases} x=-3\\ y=14 \end{cases}\implies 14=a(-3+4)^2+6$

solve for "a"