Question

Write each function in vertex form, and identify its vertex. F(x)=x^2–6x+17

Answer 1

We have to find the vertex and write the equation in vertex form.

The equation is:

`f(x)=x^2-6x+17`

We start by calculating the coordinates of the vertex (h,k):

`h=-(b)/(2a)=(-(-6))/(2\cdot1)=(6)/(2)=3`
`k=f(h)=3^2-6\cdot3+17=9-18+17=8`

The vertex form is:

`\begin{gathered} f(x)=a(x-h)^2+k \\ f(x)=(x-3)^2+8 \end{gathered}`

Answer:

Vertex: (3,8)

Vertex form: f(x)=(x-3)^2+8