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

Question

asked Oct 1, 2023 85.6k views

1 Answer

Daiwen · Answer 1 · 2023-10-05T19:44:19+0000

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

The equation is:

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