Question

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

Answer 1

Vertex `(2.5, -6.75)`

Axis of Symmetry `x=2.5`

Explanation:

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`

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