Question

Use the vertex (h, k) and a point on the graph (x, y) to find the general form of the equation of the quadratic function.(h, k) = (1, 0), (x, y) = (0, 1)f(x) =

Answer 1

A quadratic equation can be written in the vertex form to be:

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

where (h, k) is the vertex.

The question gives the following parameters:

`\begin{gathered} (h,k)=(1,0) \\ (x,y)=(0,1) \end{gathered}`

We can use these values to solve for a:

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

Therefore, the vertex form of the quadratic equation will be:

`y=(x-1)^2`

Expanding, we have the general form of the quadratic equation to be:

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