What is the equation of the following graph in vertex form

Question

asked Apr 16, 2019 107k views

1 Answer

Azar · Answer 1 · 2019-04-20T04:52:26+0000

Answer:

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.