The Discriminant

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is a value calculated from the coefficients of a quadratic equation in the form ax² + bx + c. It is given by the formula D = b² - 4ac.

Front

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

Back

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

Front

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

Back

A negative discriminant indicates that the quadratic equation has no real solutions, only complex solutions.

Front

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

Back

A zero discriminant indicates that the quadratic equation has exactly one real solution (a repeated root).

Front

Calculate the discriminant for the quadratic equation: 2x² + 3x + 1 = 0.

Back

D = 3² - 4(2)(1) = 9 - 8 = 1 (Positive, two solutions).

Front

Calculate the discriminant for the quadratic equation: x² - 4x + 4 = 0.

Back

D = (-4)² - 4(1)(4) = 16 - 16 = 0 (Zero, one solution).

Front

Calculate the discriminant for the quadratic equation: x² + 2x + 5 = 0.

Back

D = 2² - 4(1)(5) = 4 - 20 = -16 (Negative, no real solutions).

Front

What is the formula for the discriminant?

Back

The formula for the discriminant is D = b² - 4ac.

Front

If the discriminant is 0, what can be said about the vertex of the parabola?

Back

If the discriminant is 0, the vertex of the parabola touches the x-axis at the root, indicating a double root.

Front

How does the discriminant affect the graph of a quadratic function?

Back

The discriminant determines the number and type of x-intercepts of the graph of the quadratic function.