1. Graphing a Radical Function

2. Graph The domain is x > -2. The range is y > 0.

3. Solving a Radical Equation Graphically
The solution will be the
intersection of the graph
Solve
and the graph of
y = 0.
The solution
is x = 12.
Check:
L.S R.S.

4. Solving a Radical Equation Graphically
Solve
The solution is
x = 3 or x = 7.

5. Solving Radical Inequalities
Solve
Find the values for which
the graph of
Note the radical
7x - 3 is defined only
when
is above the graph of
y = 3.
The graphs intersect at
x = 4.
x > 4
Therefore, the solution
is x > 4.

6. Solving Radical Equations
Solve
x ≥ -2
Set up the equation so that
there will be one radical on
each side of the equal sign.
Square both sides.
2x + 4 = x + 7
x = 3
Simplify.
L.S R.S.
Verify your solution.
Therefore, the
solution is
x = 3.

7. Squaring a Binomial (a + 2)2 = a2 + 4a + 4 ( 5 + √x - 2 )2 (a√x + b)2
Note that the middle term is
twice the product of the two
terms of the binomial.
(a + 2)2 = a2 + 4a + 4
( 5 + √x - 2 )2
The middle term will
be twice the product
of the two terms.
A final concept that you
should know:
(a√x + b)2
= a2(x + b)
= a2x + ab

8. Solving Radical Equations
Set up the equation
so that there will be
only one radical on
each side of the equal sign.
Solve
Square both sides
of the equation.
Use Foil.
Simplify.
Simplify by dividing
by a common factor of 2.
Square both sides of the
equation.
Use Foil.

9. x - 3 = 0 or x - 7 = 0 x = 3 or x = 7 Solving Radical Equations
Distribute the 4.
Simplify.
Factor the quadratic.
Solve for x.
x - 3 = 0 or x - 7 = 0
x = 3 or x = 7
Verify both solutions.
L.S R.S.
L.S R.S.

10. Solving Radical Inequalities
Solve
x > -1
The graphs intersect
at the point where
x = 8.
x ≥ -1 and x < 8
The solution is
-1 < x and x < 8.