What is the axis of symmetry and vertex for the graph #y=x^2-8x+3#?

1 Answer
Tony B
Apr 20, 2016

#color(blue)("Vertex"->(x,y)->(4,-13)#
#color(blue)("Axis of symmetry"->x=4)#

Explanation:

Standard form:#" "y=ax^2+bx+c#

Write as:#" "y=a(x^2+b/a x)+c#

With a quadratic, the axis of symmetry passes through #x_("vertex")#

In the case of this question #a=1#

#color(blue)(x_("vertex")=(-1/2)xxb/a " "-> (-1/2)xx(-8)=+4)#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
By substitution:

#color(blue)(y_("vertex")=(4)^2-8(4)+3 =-13)#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Vertex"->(x,y)->(4,-13)#
#color(blue)("Axis of symmetry"->x=4)#

Tony B

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