Question

What is the axis of symmetry and vertex for the graph `f(x)=3x^2 - 15x + 3`?

Answer 1

vertex: (2.5, -15.75)
axis of symmetry: x=2.5

Explanation:

`f(x) = 3x^2-15x+3`
`f(x) =3[x^2-5x]+3`
`f(x)= 3[(x-5/2)^2-25/4]+3`
`f(x) = 3(x-5/2)^2-75/4+3`
`f(x)=3(x-5/2)^2-15 3/4`

`x-5/2=0`
`x=5/2`

`f(x) = 3(0)^2 -15 3/4`
`f(x)=-15 3/4`

`therefore vertex: (5/2, -15 3/4)`
`therefore "axis of symmetry": x=5/2`