Quadratic Functions and Graphs

Front

What is a quadratic function?

Back

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

Front

What is the standard form of a quadratic function?

Back

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

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point on the graph of a quadratic function, depending on whether it opens upwards or downwards.

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the equation x = -b/(2a).

Front

What does it mean if a quadratic function opens upwards?

Back

If a quadratic function opens upwards, it means the coefficient 'a' is positive, and the vertex represents the minimum point.

Front

What does it mean if a quadratic function opens downwards?

Back

If a quadratic function opens downwards, it means the coefficient 'a' is negative, and the vertex represents the maximum point.

Front

How do you find the x-intercepts of a quadratic function?

Back

The x-intercepts can be found by setting f(x) = 0 and solving the quadratic equation ax² + bx + c = 0.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of a quadratic equation.

Front

What is the discriminant in a quadratic equation?

Back

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

Front

What does a positive discriminant indicate?

Back

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