Solving Quadratics Using the Quadratic Formula

Mrs. Hayes introduces the quadratic formula to solve quadratic equations, focusing on finding zeros or solutions. She explains the formula's components, including the discriminant, and demonstrates solving an example problem. The lesson covers calculating the discriminant, simplifying solutions, and verifying results using a calculator. Students are encouraged to follow along with examples and practice using the quadratic formula.

What is the primary goal when using the quadratic formula?

• To identify the graph's symmetry

• To calculate the coefficient of the quadratic term

• To find the maximum value of the quadratic function

• To determine the zeros of the quadratic equation

What does the discriminant in the quadratic formula help determine?

• The product of the roots

• The sum of the roots

• The coefficient of the linear term

• The number of real solutions

In the equation x^2 - 2x - 4 = 0, what is the value of 'a'?

• -4

• -2

• 1

• 2

How do you calculate the discriminant?

• B^2 + 4ac

• 4ac - B^2

• 2a - B^2

• B^2 - 4ac

What is the correct application of the quadratic formula to the given equation?

• x = -B ± √(B^2 + 4AC) / 2A

• x = B ± √(B^2 + 4AC) / 2A

• x = -B ± √(B^2 - 4AC) / 2A

• x = B ± √(B^2 - 4AC) / 2A

What is the significance of the '±' symbol in the quadratic formula?

• It denotes the potential for one or two solutions

• It represents the uncertainty in the coefficient values

• It signifies that there can be two different roots

• It indicates the possible fluctuation of the discriminant

What does a discriminant value of 20 indicate about the roots?

• There are no real roots

• There are two distinct real roots

• There is one real root

• The roots are complex numbers

What is the simplified form of the square root of 20?

• 2√10

• 2√5

• 4√5

• √5

What are the solutions to the equation x^2 - 2x - 4 = 0 in simplest radical form?

• x = 1 ± 2√5

• x = 2 ± √5

• x = 1 ± √5

• x = -1 ± √5

How do you simplify the expression 2 ± √20 / 2?

• 1 ± 2√5

• 2 ± 2√5

• 1 ± √5

• 2 ± √5