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Write a quadratic function whose graph has the given characteristics.Vertex: (1,2)Point: (3,6)

Write a quadratic function whose graph has the given characteristics.Vertex: (1,2)Point-example-1
User Chintan Kukadiya
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1 Answer

14 votes
14 votes

The given point is (3,6), and the vertex is (1,2). This means


\begin{gathered} x=3,y=6 \\ h=1,k=2 \end{gathered}

We use the vertex form of a quadratic function.


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

Let's replace the given values to find a.


\begin{gathered} 6=a(3-1)^2+2 \\ 6=a(2)^2+2 \\ 6-2=4a \\ a=(4)/(4)=1 \end{gathered}

Once we have a, we can write the function using the vertex-form and the vertex point.


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

Hence, the function is


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

User Rowell
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