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Write a quadratic function whose graph passes through (2,1) and has the vertex (4,-2) y=

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The given point is (2,1), and the vertex is (4, -2). This means h = 4, and k = -2.

To find the equation, we have to find the parameter a with the given information and the vertex form.


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

Let's replace the given point and the vertex.


\begin{gathered} 1=a(2-4)^2-2 \\ 1+2=a(-2)^2 \\ 4a=3 \\ a=(3)/(4) \end{gathered}

Now, we replace the parameter a and the vertex to find the equation of the parabola.


y=(3)/(4)(x-4)^2-2

The image below shows the parabola.

The function would be


f(x)=(3)/(4)(x-4)^2-2

Write a quadratic function whose graph passes through (2,1) and has the vertex (4,-2) y-example-1
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