Question

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

Answer 1

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.

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

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

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