Solving Equations and Functions

The video tutorial covers solving radical equations, starting with an introduction to the topic. It includes examples of solving simple radical equations, rewriting formulas, and identifying extraneous solutions. The tutorial also addresses solving equations with rational expressions. The instructor emphasizes the importance of isolating radicals and checking for extraneous solutions. The video concludes with a brief wrap-up and a preview of the next class.

What is the first step in solving a radical equation?

• Multiply both sides by a constant

• Divide both sides by a constant

• Isolate the radical

• Add a constant to both sides

In Example 1, what operation is used to eliminate the square root symbol?

• Multiplying by the square root

• Squaring both sides

• Dividing by the square root

• Taking the cube root

What is the final value of x in Example 1?

• 4

• 8

• 2

• 6

In Example 2, what is the formula for stopping distance in terms of vehicle speed?

• D = 3.57 * V^2

• D = V / 3.57

• D = (V / 3.57)^2

• D = V^2 / 3.57

What is the approximate value of 3.57 squared?

• 10.24

• 12.74

• 16.00

• 14.29

What is an extraneous solution?

• A solution that satisfies the original equation

• A solution that does not satisfy the original equation

• A solution that is always positive

• A solution that is always negative

In Example 3, which value of x is an extraneous solution?

• 4

• 8

• -1

• 6

In Example 4, what power is used to eliminate the three-halves exponent?

• 2/3

• 3/2

• 1/2

• 1/3

What is the value of 8 raised to the 2/3 power?

• 8

• 4

• 2

• 16

What are the solutions to the quadratic equation in Example 4?

• 5 and -2

• 5 and 2

• 4 and -2

• 4 and 2