Lesson 3 Absolutely Valuable Solidify Understanding

Ready

Describe the transformations of $y = x^{2}$ that produce the given function.

1.

$y = {(x - 2)}^{2} - 9$

2.

$y = - {(x + 3)}^{2} + 9$

3.

$y = {(x - 1)}^{2} - 2$

Rewrite the function in vertex form. Then describe the transformation on $y = x^{2}$ .

4.

$y = x^{2} + 4 x - 10$

5.

$y = x^{2} + 8 x + 7$

6.

$y = 2 x^{2} + 12 x + 20$

Set

Use the given function rule to fill in the table of values.

7.

$g (x) = | x - 1 |$

$x$	$g (x)$
$- 2$
$- 1$
$0$
$1$
$2$

8.

$f (x) = | x + 1 |$

$x$	$f (x)$
$- 2$
$- 1$
$0$
$1$
$2$

9.

$h (x) = | x | + 1$

$x$	$- 2$	$- 1$	$0$	$1$	$2$
$h (x)$

10.

$p (x) = | x | - 1$

$x$	$- 2$	$- 1$	$0$	$1$	$2$
$p (x)$

Show how the graph of the given function would change if absolute value was applied to the entire original function. Sketch on top of the given graph and indicate where the new function would be the same and where it would be different.

11.

12.

13.

Go

Evaluate each expression for the given value of the variable.

14.

$- s; s = 4$

15.

$- t; t = - 7$

16.

$- x; x = 0$

17.

$- w; w = - 11$

18.

$| v |; v = - 25$

19.

$- (a); a = - 25$

20.

$- (- n); n = - 2$

21.

$| - (- p) |; p = - 6$

22.

$| - (- q) |; q = 8$

23.

$- | - (- r) |; r = - 9$