Question

How can you help me with the equation in the photo?

Answer 1

The given expression is

`y=x^2-2x+2`

First, we find the vertex (h,k) where a = 1, b = -2, and c = 2.

`\begin{gathered} h=-(b)/(2a)=-(-2)/(2\cdot1)=1 \\ k=f(1)=(1)^2-2(1)+2=1-2+2=1 \end{gathered}`

So, the vertex is at (1,1), the vertex form would be

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

The expression has minium (1,1), its opening upside and it doesn't have intercepts.

The image below shows the graph

Hence, the previous analysis was correct.