Solving Quadratic Equations with Square Roots

Betsy introduces quadratic equations, explaining their characteristics and how to identify them. She demonstrates solving two quadratic equations using square roots, emphasizing the importance of performing operations on both sides of the equation. The video concludes with graphing the solutions and identifying x-intercepts.

What is the highest exponent that defines a quadratic equation?

• 1

• 2

• 3

• 4

What does the degree of a quadratic equation indicate?

• Highest exponent

• Constant term

• Coefficient of x

• Number of solutions

What operation is used to simplify the equation x - 4^2 = 36?

• Subtraction

• Addition

• Square root

• Multiplication

What value of x satisfies the equation when x - 4 = 6?

• 2

• 6

• 10

• -2

What are the solutions to the equation x - 4^2 = 36?

• 6 and -6

• 2 and -2

• 10 and -6

• 10 and -2

How do you eliminate the squared term in the equation 3(x - 5)^2 = 75?

• Square root

• Subtract 5

• Add 3

• Divide by 3

What is the result of square rooting both sides of x - 5^2 = 25?

• x - 5 = 0

• x - 5 = -5

• x - 5 = 25

• x - 5 = 5

Which operation is used first to solve the equation 3(x - 5)^2 = 75?

• Multiplication

• Division

• Addition

• Subtraction

What values of x satisfy the equation x - 5 = 5?

• 10

• 5

• 15

• 0

What are the x-intercepts of the quadratic equation represented by 3(x - 5)^2 = 75?

• 0 and 10

• -5 and 5

• 10 and 0

• 5 and 10