# 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 \(f(2) = f(3)\).

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

### 23.3: Finding the Vertex

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

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