The Discriminant

Front

What is the Discriminant in a quadratic equation?

Back

The Discriminant is the part of the quadratic formula under the square root, given by b² - 4ac, which determines the nature of the roots of the equation.

Front

How do you calculate the Discriminant for the quadratic equation ax² + bx + c = 0?

Back

The Discriminant is calculated using the formula D = b² - 4ac.

Front

What does a positive Discriminant indicate about the roots of a quadratic equation?

Back

A positive Discriminant indicates that there are two distinct real solutions (roots) for the quadratic equation.

Front

What does a Discriminant of zero indicate about the roots of a quadratic equation?

Back

A Discriminant of zero indicates that there is exactly one real solution (a repeated root) for the quadratic equation.

Front

What does a negative Discriminant indicate about the roots of a quadratic equation?

Back

A negative Discriminant indicates that there are two complex (non-real) solutions for the quadratic equation.

Front

If a quadratic equation has a Discriminant of 57, what can be inferred about its roots?

Back

Since 57 is positive, the quadratic equation has two distinct real solutions.

Front

If a quadratic equation has a Discriminant of -44, what can be inferred about its roots?

Back

Since -44 is negative, the quadratic equation has two complex solutions.

Front

What is the significance of the coefficients a, b, and c in the Discriminant formula?

Back

The coefficients a, b, and c are the numerical values from the quadratic equation ax² + bx + c = 0, where 'a' is not zero.

Front

How can the Discriminant help in graphing a quadratic function?

Back

The Discriminant helps determine the number of x-intercepts (real roots) of the quadratic function, which affects its graph.

Front

What is the relationship between the Discriminant and the vertex of a parabola?

Back

The Discriminant does not directly affect the vertex, but it indicates the number of real solutions, which can influence the position of the parabola relative to the x-axis.