Radical Functions and Equations

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be twice the product

of the two terms.

A final concept that you

should know:

= a2x + ab

= a2(x + b)

Slide 15

Set up the equation

so that there will be

only one radical on

each side of the equal sign.

Square both sides

of the equation.

Simplify.

Simplify by dividing

by a common factor of 2.

Square both sides of the

equation.

Use Foil.

Use Foil.

Solve

Solving Radical Equations

Slide 16

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.

Solving Radical Equations

L.S. R.S.

L.S. R.S.

Slide 17

One more to see another extraneous solution

The radical is already isolated

2

2

You must square the whole side NOT each term.

Square both sides

Since you have a quadratic equation (has an x2 term) get everything on one side = 0 and see if you can factor this

You MUST check these answers

This must be FOILed

Doesn't work! Extraneous

It checks!

Slide 18

Let's try another one

First isolate the radical

- 1

- 1

3

3

Now since it is a 1/3 power this means the same as a cube root so cube both sides

Now solve for x

- 1

- 1

Let's check this answer

It checks!

Remember that the 1/3 power means the same thing as a cube root.

Slide 19

Graphing a Radical Function

Graph

The domain is x > -2.

The range is y > 0.

Slide 20

Solving a Radical Equation Graphically

Solve

The solution will be the

intersection of the graph

and the graph of

y = 0.

The solution

is x = 12.

Check:

0

L.S. R.S.

Slide 21

The solution is

x = 3 or x = 7.

Solve

Solving a Radical Equation Graphically

Slide 22

Solving Radical Inequalities

Find the values for which

the graph of

is above the graph of

y = 3.

The graphs intersect at

x = 4.

Note the radical

7x - 3 is defined only

when .

Therefore, the solution

is x > 4.

x > 4

Solve

Slide 23

The solution is