Quadratic Functions: Roots and Discriminant

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically expressed in the form f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What are the roots of a quadratic function?

Back

The roots of a quadratic function are the values of x for which the function equals zero, i.e., the points where the graph intersects the x-axis.

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 D = b² - 4ac. It determines the nature and number of roots of the quadratic equation.

Front

What does a positive discriminant indicate?

Back

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

Front

What does a zero discriminant indicate?

Back

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

Front

What does a negative discriminant indicate?

Back

A negative discriminant indicates that the quadratic equation has no real roots, but two complex roots.

Front

How can you find the roots of a quadratic function using factoring?

Back

To find the roots using factoring, express the quadratic in the form (x - r1)(x - r2) = 0, where r1 and r2 are the roots, and solve for x.

Front

What is the vertex of a quadratic function?

Back

The vertex of a quadratic function is the highest or lowest point on the graph, depending on the direction of the parabola, and can be found using the formula (-b/2a, f(-b/2a)).

Front

How do you determine the axis of symmetry for a quadratic function?

Back

The axis of symmetry for a quadratic function is a vertical line that passes through the vertex, given by the equation x = -b/2a.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax² + bx + c.