Download Domain - solve for variable under radical to find domain

UNIT 3 LESSON 5
RADICAL EQUATIONS AND SQUARE ROOT FUNCTION
Solving Radical Equations
A “radical” equation is when the variable is in the radicand.
How to:
Step 1: Isolate the radical
Step 2: Raise each side to power equal to index
Step 3: Solve the resulting equation
Step 4: Check answers to avoid extraneous solutions (extraneous means that the solution does not work)
Ex 4) Simplify
Step 1: Is radical isolated? YES because there are no constants or variables in front or behind radical
Step 2: The index = 2 so we will square both sides of the equation
( √𝑥 − 1) 2 = (2) 2
Step 3: Solve the equation
x – 1= 4
x=5
Step 4: Check for extraneous solutions (plug x = 5 into original equation)
2 = 2 My solution checks good. x = 5 is the solution to the equation
√5 − 1 = 2
√4 = 2
Ex 5) Simplify
(x − 3) 2 = (√30 − 2𝑥) 2
X2 – 6x + 9 = 30 – 2x
X2 – 4x -21 = 0
(x – 7) (x + 3) = 0
x =7 x = -3
x=7 is a solution to the equation, x = -3 is an extraneous solution
Check:
7 − 3 = √30 − 2(7)
−3 − 3 = √30 − 2(−3)
4 = √16
4 =4
-6 = √36
-6 = 6
Domain - solve for variable under radical to find domain
We will graph the square root function using transformation rules.
Example 1) Graph the function
State the transformation and domain
Using the graphing calculator, input the function. Notice the transformation from the original function (square
root function) and the function given.
Answer: Graph moves right 2 units. Domain = x ≥ 2
Example 2) Graph the function
State the transformation and domain
Using the graphing calculator, input the function. Notice the transformation from the original function (square
root function) and the function given.
Answer: Graph moves right 3 units, up 2 units, and reflection. Domain = x ≥ 3