Exploring the Quadratic Formula and Discriminant

What is the quadratic formula derived from?

• Synthetic division

• Graphing

• Factoring

• Completing the square

In the quadratic formula, what does 'b' represent?

• The constant term

• The coefficient of x^2

• The discriminant

• The coefficient of x

What is the first step in solving a quadratic equation using the quadratic formula?

• Graphing the equation

• Factoring the equation

• Putting the equation in standard form

• Finding the vertex

What is the result when the discriminant is zero?

• No real roots

• Two complex roots

• One real root

• Two real roots

What is the simplified form of the quadratic formula solution for a = 1, b = -16, and c = 64?

• 16

• 0

• -8

• 8

When do most people prefer to use the quadratic formula?

• When the factoring methods are not working

• When the equation has complex roots

• When the equation is in vertex form

• When the equation is easily factorable

What is the nature of the roots if the discriminant is a positive perfect square?

• Two complex roots

• One real root

• Two real irrational roots

• Two real rational roots

What is the nature of the roots if the discriminant is a positive non-perfect square?

• Two real irrational roots

• Two complex roots

• Two real rational roots

• One real root

What is the nature of the roots if the discriminant is negative?

• Two complex roots

• Two real irrational roots

• Two real rational roots

• One real root

What is the discriminant of the equation 8^2 - 4 * -5 * -1?

• 16

• 64

• 44

• 20