Lesson 23

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

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

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

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

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

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

4. 

   

5. 

   

6. 

   

7. 

   

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. $y = 2x^2 - 12x + 22$

7.