# Lesson 23

Comparing Functions

• Let’s evaluate and compare functions.

### 23.1: Math Talk: Evaluating Functions

Mentally evaluate each of the functions when $$x = 3$$.

$$f(x) = x^2 - 4x + 1$$

$$g(x) = 6x - 2x^2$$

$$h(x) = (x-4)(x-3)$$

$$j(x) = 2(x-1)(x+2)$$

### 23.2: Comparing Functions

The notation $$f(2)$$ means the output of function $$f$$ when $$x$$ is 2. For each function, determine whether $$f(2) > f(3)$$, $$f(2) < f(3)$$, or $$f(2) = f(3)$$.

1. $$f(x) = x^2 + 2x+ 3$$
2. $$f(x) = (x-2)(x-3)$$
3. $$f(x) = \text{-}x^2 + 5$$

### 23.3: Finding the Vertex

Write each function in vertex form, then find the coordinates of the vertex.

1. $$y = x^2 - 4x + 7$$
2. $$y = (x-1)(x+3)$$
3. $$y = (x-2)(x+2)$$
4. $$y = x^2 - 2x + 1$$
5. $$y = \text{-}x^2 -2x-6$$
6. $$y = 2x^2 - 12x + 22$$