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

1 Answer
Jun 10, 2015

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]}