Question

How do you graph and identify the vertex and axis of symmetry for `y=x^2-4x+7`?

Answer 1

Complete the Square

Explanation:

Firstly we should complete the Square

`therefore` `x^2-4x+7 = (x-2)^2-4+7 = (x-2)^2+3`

Now we have can identify the vertex which would be...

`(2,3)` graph{x^2 -4x+7 [-10, 10, -5, 5]} and from this we can find the axis of symmetry `x=2`

Sketching the graph would be harder as it has no roots so we can only go with the `C` value, the `7` and the minimum. Plot these points and carefully sketch the graph.