Question

the vertex of this parabola is at (-2,-3). What is the coefficient of the squared term in the parabola's equation?

Answer 1

`\bf \textit{parabola vertex form}\\\\ \boxed{y=a(x-{{ h}})^2+{{ k}}}\\\\ x=a(y-{{ k}})^2+{{ h}}\qquad\qquad vertex\ ({{ h}},{{ k}})\\\\ -----------------------------\\\\ y=a(x-h)^2+k\qquad \begin{cases} h=-2\\ k=-3 \end{cases}\implies y=a[x-(-2)]^2-3 \\\\\\ y=(x+2)^2-3`

expand the binomial, either binomial theorem, or just FOIL

bear in mind, we're assuming the coefficient "a" is 1
and we're also assuming is the first form, it could be the second, but we're assuming is a vertical parabola