How do you find the axis of symmetry, graph and find the maximum or minimum value of the function #y=x^2+6x+2#?

Question

1530 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-12-12T04:51:40

#x=-3" " # is the axis of symmetry

the vertex of the parabola is at #(h, k)=(-3, -7)#
by the formula

#h=-b/(2a)# and #k=c-b^2/(4a)#

from the given #y=x^2+6x+2#
#a=1#, #b=6#, and #c=2#

#h=-b/(2a)=-6/(2*1)=-3#

#k=c-b^2/(4a)=2-6^2/(4*1)=2-36/4=2-9=-7#

The minimum point is the vertex #(-3, -7)#
graph{y=x^2+6x+2 [-13.58, 6.42, -8.6, 1.4]}

and clearly #x=-3# a vertical line which passes thru #(-3, -7)# is the line of symmetry.

God bless....I hope the explanation is useful.