Question

Write the equation of the parabola that has the vertex at point (2,7) and passes through the point (−1,3).

Answer 1

$\bf ~~~~~~\textit{parabola vertex form} \\\\ \begin{array}{llll} \boxed{y=a(x- h)^2+ k}\\\\ x=a(y- k)^2+ h \end{array} \qquad\qquad vertex~~(\stackrel{}{ h},\stackrel{}{ k})\\\\ -------------------------------\\\\ vertex~(\stackrel{h}{2},\stackrel{k}{7})\qquad y=a(x-2)^2+7 \\\\\\ \textit{we also know it passes through }(\stackrel{x}{-1},\stackrel{y}{3})\qquad 3=a(-1-2)^2+7 \\\\\\ 3=a(-3)^2+7\implies 3=a9+7\implies -4=9a\implies \cfrac{-4}{9}=a \\\\\\ therefore\qquad \boxed{y=-\cfrac{4}{9}(x-2)^2+7}$

Answer 2

Answer:

y=-4/9(x-2)^2+7

Step-by-step explanation: