Question

the vertex of this parabola is at (3,5). When the y-value is 6, the x-value is -1. What is the coefficient of the squared term in the parabolas equation

Answer 1

Now, assuming is a vertical parabola, so the squared variable is the "x", let's do some checking.

$\bf \qquad \textit{parabola vertex form}\\\\ \begin{array}{llll} \boxed{y=a(x-{{ h}})^2+{{ k}}}\\\\ x=a(y-{{ k}})^2+{{ h}} \end{array} \qquad\qquad vertex\ ({{ h}},{{ k}})\\\\ -------------------------------\\\\ vertex \begin{cases} h=3\\ k=5 \end{cases}\implies y=a(x-3)^2+5 \\\\\\ \textit{we also know that } \begin{cases} y=6\\ x=-1 \end{cases}\implies 6=a(-1-3)^2+5 \\\\\\ 1=a(-4)^2\implies 1=16a\implies \cfrac{1}{16}=a$