12.02 and 12.03 Determine 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 the expression b² - 4ac, which determines the nature of the roots of the equation.

Front

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

Back

A positive discriminant indicates that the quadratic equation has two distinct real roots.

Front

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

Back

A negative discriminant indicates that the quadratic equation has two complex (imaginary) roots.

Front

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

Back

A discriminant of zero indicates that the quadratic equation has exactly one real root, also known as a repeated or double root.

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

If the discriminant is positive, how many x-intercepts does the graph of the quadratic function have?

Back

If the discriminant is positive, the graph of the quadratic function has two x-intercepts.

Front

If the discriminant is negative, what can be said about the graph of the quadratic function?

Back

If the discriminant is negative, the graph of the quadratic function does not intersect the x-axis.

Front

What is the quadratic formula used to find the roots of a quadratic equation?

Back

The quadratic formula is x = (-b ± √D) / (2a), where D is the discriminant.

Front

Solve the quadratic equation x² + 4x + 5 = 0 using the quadratic formula.

Back

The discriminant D = 4² - 4(1)(5) = 16 - 20 = -4. The roots are x = -2 ± 3i.

Front

What is the significance of the vertex in a quadratic function?

Back

The vertex is the highest or lowest point of the parabola, depending on whether it opens upwards or downwards.