How do you graph and label the vertex and axis of symmetry of #y=3(x-1)(x-4)#?

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Answer 1 · 2017-07-17T05:47:18

Vertex #(2.5, -6.75)#

Axis of Symmetry #x=2.5#

Given -

#y=3(x-1)(x-4)#

Let us rewrite it as -

#y=(3x-3)(x-4)#
#y=3x^2-3x-12x+12#
#y=3x^2-15x+12#

Vertex -

#x=(-b)/(2a)=(-(-15))/(2 xx 3)=15/6=5/2#

At #x=5/2=2.5#

#y=3(2.5)^2-15(2.5)+12#
#y=18.75-37.5+12=-6.75#

Vertex #(2.5, -6.75)#

Axis of Symmetry #x=2.5#

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Take a few values on either side of #x=2.5#
Find the corresponding y value. Tabulate them and plot them.

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