Question

What is the equation of the following graph in vertex form

Answer 1

Answer:

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

Step-by-step 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.