sorry that their wasnt anything posted, well now i will. In the couple of days we learned about Radical Equation and absolute value equations and graphing absolute values.
Here are a couple of examples from the booklets we got:
Radical Equation
(2√9k - 9)2 = (18)2 First you square both sides, which cancels the √
4(9k - 9) = 324 Then you multiply the 4 to the brackets
36k -36 = 324 After that move the 36 to the other side
36k = 360 Divide both sides by 36
k = 10 Final answer is 10
After that is done we need to check
2√9(10) - 9 = 18
2√90 - 9 = 18
2√81 = 18
2(9) = 18
18 = 18
so the value for k is 10
example 2 :
√b + 1 - 4 = 6 Move the 4 over
√b + 1 = 10 You square both sides, which cancels the √
b + 1 = 100 Move the 1 over
b = 99 The answer is 99
check
√99 + 1 - 4 = 6
√100 - 4 = 6
10 - 4 = 6
6 = 6
so the solution is b = 99
Now lets do Absolute Value equations
First example
⎥X + 8⎥ = 1
(x + 8) = 1
X = -7
Or
-⎥X + 8⎥ = 1
-X - 8 = 1
-X = 9
Now lets check
⎥-7 + 8⎥ = 1
⎥1⎥ = 1
⎥-9 + 8⎥ = 1
⎥-1⎥ = 1
1 = 1
X can equal -7 and -9
Now lets go to our second example
⎥6n⎥ = 24
⎥n⎥ = 4
Check
⎥6(4)⎥ = 24
⎥24⎥ = 24
Or
⎥6n⎥ = 24
⎥n⎥ = -4
Check
⎥6(-4)⎥ = 24
⎥-24⎥ = 24
⎥24⎥ = 24
n can equal -4 or 4
Graphing absolute value graph
An absolute value of a function means, only the positive value of the function will be draw since absolute values are positive.
That is if y = lxl, y is positive even for negative values of x. For example if x = -1, then y = l-1l = 1 then the -1 changes to 1. Let us see the change in the graphs when the function is defined as y = lxl
Figure 1 shows the graph of the function y = x and figure 2 shows the function y = lxl. In figure 2, the portion below the x- axis is just reflected above the x- axis.
y = lx + 3l - 1, the graph would be like this.
No comments:
Post a Comment