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Use the vertex ( h, k ) and a point on the graph ( x, y ) to find the standard form of the equation of the quadratic function:Vertex = (-4,2)Point = (-4,0)F( x )= Answer for coordinate 1 (x- Answer for coordinate 2 )^2 +Answer for coordinate 3

Use the vertex ( h, k ) and a point on the graph ( x, y ) to find the standard form-example-1

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In order to find the quadratic equation, let's use the vertex form below:


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

Where the vertex is located at (h, k).

So, if the vertex is (h, k) = (-4, 2) and using the point (x, y) = (-4, 0), we have:


\begin{gathered} y=a(x+4)^2+2 \\ 0=a(-4+4)^2+2 \\ 0=a\cdot0^2+2 \\ 0=2 \end{gathered}

Since the final statement is false, it's not possible to have a quadratic function with vertex (-4, 2) and with the point (-4, 0).

If we use the point (4, 0) instead, we would have:


\begin{gathered} y=a(x+4)^2+2 \\ 0=a(4+4)^2+2 \\ 0=a\cdot64+2 \\ 64a=-2 \\ a=-(2)/(64) \\ a=-(1)/(32) \end{gathered}

So the equation in this case would be:


y=(-(1)/(32))(x-(-4))^2+2

The empty spaces would be filled with the values -1/32, -4 and 2.

User IsraGab
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