Question

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

Answer 1

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

Explanation:

`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`