Download Algebra II Unit 2 Test 1.6: absolute value equations: 1) get the

Algebra II Unit 2 Test
1.6:
absolute value equations: 1) get the absolute value bars alone by adding, subtracting, multiplying, or dividing, 2) rewrite as 2
equations (remember 1 is positive, 1 is negative, 3) solve each equation, 4) check for extraneous solutions, 5) write answer in
set builder notation
example: 4|6x + 2 | - 2 = 30
4|6x + 2| = 32
|6x + 2 | = 8
6x + 2 = 8 or 6x + 2 = -8
6x = 6
or 6x = -10
x=1
or x = -5/3
check: 4|6(1) + 2| -2 = 30
4|6(-5/3) +2 | - 2= 30
4|8| -2 = 30
4|-8| -2 = 30
4(8) – 2 = 30
4(8) -2 = 30
30 = 30
30 = 30
|2x – 6| = 3x – 5
2x – 6 = 3x – 5 or 2x - 6 = -3x + 5
-6 = x – 5
or 5x - 6 = 5
-1 = x
or
5x = 11
x = 11/5
Answers: {x | x = 1 or x = -5/3}
{x |x= 8/5}
|2(-1) – 6| = 3(-1) – 5
|-8| = -8
8 ≠ -8
|2(11/5) – 6| = 3(11/5) – 5
|-8/5| = 8/5
8/5 = 8/5
Absolute value inequalities: |x| > # or |x| >: or statements: x > # or x < - #
|x| < # or |x|<: and statement: - # < x < #
Examples: 1) |x + 4| > 7
x + 4 > 7 or x + 4 < -7
x > 7 or x < -11
(7, ∞) U (-∞, -11)
-11
0
7
|2x – 4| < 10
-10 < 2x – 4 < 10
+4
+4 +4
-6 < 2x < 14
-3 < x < 7
[-3, 7]
-3
0
7
2.5 Scatter plots:
- be able to identify the type of correlation shown: strong negative, weak negative, no correlation, weak positive and strong
positive (this is matching on the test)
-make a scatter plot, draw a line of best fit, find the equation of the line of best fit, and make a prediction based on your
equation
** to write the equation: 1) pick any 2 points on your line of best fit, 2) find the slope of those points, 3) pick 1 of your 2
points and the slope and find b by plugging your m and (x, y) into y = mx + b, 4) write the equation of the line (remember
only m & b become numbers)
2.6/2.7: graphing transformations:
This concept summary will work with any parent function
*remember f(x) = y
Graph and describe transformation
y = (x – 1)2 + 1
description: shifts up 1 and to the right 1
y = -|x + 2| + 3
description: reflection over the x-axis, shifts up 3 and left 2