Question

How do you graph the parabola `y=x^2 - 4x +7` using vertex, intercepts and additional points?

Answer 1

The vertex is `(2,3)`
The y intercept is `(0,7)`

Explanation:

let's rewrite the equation in the vertex form
`y=x^2-4x+4+7-4=(x-2)^2+3`
`(x-2)^2=y-3`
The equation of a parabola is `(x-a)^2=2p(y-b)`
Here `2p=1` `=>` `p=1/2`
So the vertex is `(2,3)`
The focus is `(2,7/2)`
And the directrix is `y=5/2`
The y intercept is when `x=0` `=>`y=7#
graph{x^2 -4x+7 [-9.62, 12.88, -0.31, 10.95]}