Question

What is the standard quadratic form if the vertex is (4,7) and in case yo need it another value is (6,19). I REALLY NEED THIS PLEASE!!!

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Answer 1

`~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{`

`vertex \begin{cases} x=4\\ y=7 \end{cases}\implies y=a(x-4)^2 +7~\hfill \textit{we also know that} \begin{cases} x=6\\ y=19 \end{cases} \\\\\\ 19~~ = ~~a(6-4)^2 +7\implies 12=a(2)^2\implies \cfrac{12}{(2)^2}=a\implies 3=a \\\\[-0.35em] ~\dotfill\\\\ ~\hfill {\LARGE \begin{array}{llll} y=3(x-4)^2 + 7 \end{array}} ~\hfill`