Question

How do you find the vertex and the intercepts for `y=2x^2 -4x +3`?

Answer 1

Vertex is `(1,1)` and intercept on `y`-axis is `3`. There is no intercept on `x`-axis.

Explanation:

Writing the equation `y=2x^2-4x+3` in vertex form

we have `y=2(x^2-2x+1-1)+3`

or `y=2((x-1)^2)+3-2`

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

Hence, vertex is `(1,1)`

As `(x-1)^2>=0`, `y>=1` and hence it does not touch `x`-axis (`y=0`) and hence we do not have any `x` intercept.

When `x=0`, `y=3` and hence `y` intercept is `3`.

graph{2x^2-4x+3 [-4.332, 5.67, -0.42, 4.58]}