Mathematics, 29.11.2021 03:40 eturner518
Write the quadratic function in f(x)=a(x−h)2+k form whose graph is shown below. The graph shows a downward facing parabola with vertex (negative 3, 4) and y-intercept (0, negative 5).
Answers: 2
![~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{o pens~\cap}\qquad \stackrel{"a"~is~positive}{o pens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill](/tpl/images/2572/6958/ef08f.png)
![(\stackrel{h}{-3}~~,~~\stackrel{k}{4})\qquad \implies f(x) = a[x-(-3)]^2+4\implies f(x) = a(x+3)^2+4 \\\\\\ \textit{we know that} \begin{cases} x=0\\ f(x) = -5 \end{cases}\implies -5=a(0+3)^2+4\implies -5=9a+4 \\\\\\ -9=9a\implies \cfrac{-9}{9}=a\implies \boxed{-1=a}~\hfill \blacktriangleright f(x)=-(x+3)^2+4 \blacktriangleleft](/tpl/images/2572/6958/97d84.png)
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Write the quadratic function in f(x)=a(x−h)2+k form whose graph is shown below.
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