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

1 Answer
Luca F.
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]}

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