Question

(PARABOLA? BRAINLIEST + 20 POINTS) A building has an entry the shape of a parabolic arch 22 ft high and 28 ft wide at the base. Find an equation for the parabola if the vertex is put at the origin of the coordinate system.

Answer 1

Check the picture below.

$\bf ~~~~~~\textit{parabola vertex form} \\\\ \begin{array}{llll} y=a(x- h)^2+ k\qquad \leftarrow \textit{let's use this one}\\\\ x=a(y- k)^2+ h \end{array} \qquad\qquad vertex~~(\stackrel{}{ h},\stackrel{}{ k}) \\\\[-0.35em] \rule{34em}{0.25pt}$

$\bf \begin{cases} h=0\\ k=0 \end{cases}\implies y=a(x-0)^2+0 \\\\\\ \textit{we also know that } \begin{cases} x=14\\ y=-22 \end{cases}\implies -22=a(14-0)^2+0 \\\\\\ -22=a(14)^2\implies -22=196a\implies \cfrac{-22}{196}=a\implies -\cfrac{11}{98}=a \\\\[-0.35em] ~\dotfill\\\\ y=a(x-0)^2+0\implies \boxed{y=-\cfrac{11}{98}x^2}$