Question

Please help!

Write the equation of the parabola in vertex form.

Vertex (2,1), point (1,-3)
f(x)=

Answer 1

`\bf ~~~~~~\textit{parabola vertex form} \\\\ y=a(x- h)^2+ k \qquad\qquad vertex~~(\stackrel{2}{ h},\stackrel{1}{ k}) \\\\[-0.35em] ~\dotfill\\\\ y=a(x-2)^2+1 \\\\\\ \textit{we know that it passes through (1,-3) } \begin{cases} x=1\\ y=-3 \end{cases}\implies -3=a(1-2)^2+1 \\\\\\ -4=a(-1)^2\implies -4=a~\hfill \boxed{y=-4(x-2)^2+1}`