Question

Can I find a tutor to help me with this answer?

Answer 1

Explanation:

We have the equation of a quadratic function:

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

And we need to find and plot the vertex of the equation.

We start by remembering that a quadratic equation is represented by a parabola and that the vertex is the point where the parabola changes direction, usually represented by (h, k) as shown in the following example:

• How do we find the vertex using the given equation?

We find it by comparing our equation with the general vertex form of the quadratic equation:

`f(x)=a(x-h)^2+k`

where

`(h,k)`

is the vertex, and a is a constant.

Using the given equation, we find the h and k values:

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

Therefore, the vertex is at (2, 2).

Answer:

The point (2,2) representing the vertex is shown in the image: