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Write a formula for the function in the image below.

Write a formula for the function in the image below.-example-1
User Archura
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The vertex form of a quadratic function is:


f(x)=a(x-h)^2+k

Where (h, k) is the vertex. Looking at the graph, the vertex is at (-1, 2), then:


\begin{gathered} h=-1 \\ k=2 \\ \Rightarrow f(x)=a(x+1)^2+2 \end{gathered}

Finally, to find "a" we use the fact that 1 is the y-intercept of the graph (where the function is evaluated at x = 0). Then:


\begin{gathered} f(0)=1\Rightarrow a(0+1)^2+2=1 \\ a=1-2 \\ \Rightarrow a=-1 \end{gathered}

The final form of the function is:


f(x)=-(x+1)^2+2

User Adrian Collado
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