Question

How do you find the vertex of the graph of the function `3x^2-18x+24`?

Answer 1

Vertex of `f(x)=3x^2-18x+24` is `(3,-3)`

Explanation:

To find the vertex of the graph of function `f(x)=3x^2-18x+24`, we should convert it into the form `f(x)=a(x-h)^2+k`, where `(h,k)` is the vertex.

Hence `f(x)=3x^2-18x+24`

= `3(x^2-6x)+24`

= `3(x^2-2xx3xx x+3^2-3^2)+24`

= `3(x-3)^2-27+24`

= `3(x-3)^2-3`

Hence, vertex of `f(x)=3x^2-18x+24` is `(3,-3)`

graph{3x^2-18x+24 [-2.02, 7.98, -3.26, 1.74]}