Question

What is the equation of the following graph in vertex form

Answer 1

The first option,
`y=(x-2)^2+1`

Explanation:

Because the graph is showing a quadratic function we need to start by the equation of a quadratic function in its vertex form, which is:

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

a= is a transformation coefficient

(h,k)=vertex coordinates

Because the vertex is (2,1) then h=2 and k=1, using the vertex form we obtain:

`y=a(x-2)^2+1`

Now, because we have an extra point (0,5), we can find 'a' as follows:

`5=a(0-2)^2+1`, which can be simplified as:

`5=4a+1`

`a=(5-1)/4`

`a=1`

Then the vertex form of the graph is:

`y=(x-2)^2+1`, which is the first option.