Question

How to graph a parabola `y = x^2 - 6x + 7`?

Answer 1

graph{x^2-6x+7 [-5, 10, -5, 10]}

Explanation:

Find the intersections :
`Delta_x=36-4*7=36-28=12=(2sqrt(3))^2`
`x_"1,2"=(6+-2sqrt(3))/2=3+-sqrt(3)`
`x_1=3-sqrt(3)~~1.27`
`x_2=3+sqrt(3)~~4.73`

`x=0 -> y=7`
So the intersections are:
`I={(0,7),(3-sqrt(3),0),(3+sqrt(3),0)}`.

Find the vertex :
`x_v=-b/(2a)=6/2=3`
`y_v=-Delta/(4a)=-12/4=-3.`
The vertex is `V(3,-3)`.

graph{x^2-6x+7 [-5, 10, -5, 10]}