What is the axis of symmetry and vertex for the graph $3x^2 -8x +7$ ?

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Answer 1 · 2017-03-17T15:57:16

Vertex $->(x,y)=(4/3,5/3)$
Axis of symmetry = $x_("vertex")=4/3$

$color(brown)("The axis of symmetry and "x_("vertex")" both have the same x-value.")$

$color(blue)("Determining the vertex")$

A sort of cheat way (not really).

Write as: $y=3(x^2-8/3x)+7$

$x_("vertex")=(-1/2)xx(-8/3) = +4/3$

Substitute $x=4/3$ giving

$y=3x^2-8x+7" "->" "y=3(4/3)^2-8(4/3)+7$

$y_("vertex")= 5/3$

Vertex $->(x,y)=(4/3,5/3)$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

$color(blue)("Determining the axis of symmetry")$

Axis of symmetry = $x_("vertex")=4/3$

Tony B

What is the axis of symmetry and vertex for the graph 3x^2 -8x +73x^2 -8x +7?