Mathematics, 30.06.2019 13:30 sierram298
Suppose a parabola has an axis of symmetry at x=-5, a maximum height of 9, and passes through the point (-7,1). write the equation of the parabola in vertex form.
Answers: 1
![\bf ~~~~~~\textit{parabola vertex form} \\\\ \begin{array}{llll} y=a(x- h)^2+ k\qquad \leftarrow \textit{using this one}\\\\ x=a(y- k)^2+ h \end{array} \qquad\qquad vertex~~(\stackrel{}{ h},\stackrel{}{ k}) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \begin{cases} h=-5\\ k=9 \end{cases}\implies y=a[x-(-5)]^2+9\implies y=a(x+5)^2+9](/tpl/images/0034/9976/012e7.png)
![\bf \textit{we also know that } \begin{cases} x=-7\\ y=1 \end{cases}\implies 1=a(-7+5)^2+9 \\\\\\ -8=a(-2)^2\implies -8=4a\implies \cfrac{-8}{4}=a\implies -2=a \\\\[-0.35em] ~\dotfill\\\\ ~\hfill y=-2(x+5)^2+9~\hfill](/tpl/images/0034/9976/cc8a3.png)
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Suppose a parabola has an axis of symmetry at x=-5, a maximum height of 9, and passes through the po...
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