Key Features of Quadratic Functions

Front

What is a quadratic function?

Back

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

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola represented by the quadratic function, depending on the direction it opens.

Front

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

Back

The axis of symmetry can be found using the formula x = -b/(2a), where a and b are coefficients from the quadratic equation in standard form.

Front

What is the domain of a quadratic function?

Back

The domain of a quadratic function is all real numbers, represented as (-∞, ∞).

Front

What is the range of a quadratic function that opens upwards?

Back

The range is all real numbers greater than or equal to the y-coordinate of the vertex, represented as [k, ∞) if the vertex is (h, k).

Front

What is the range of a quadratic function that opens downwards?

Back

The range is all real numbers less than or equal to the y-coordinate of the vertex, represented as (-∞, k] if the vertex is (h, k).

Front

What does it mean for a quadratic function to have an absolute minimum?

Back

An absolute minimum occurs at the vertex of a quadratic function that opens upwards, where the function reaches its lowest value.

Front

What does it mean for a quadratic function to have an absolute maximum?

Back

An absolute maximum occurs at the vertex of a quadratic function that opens downwards, where the function reaches its highest value.

Front

How can you determine if a quadratic function opens upwards or downwards?

Back

If the coefficient 'a' in the quadratic function f(x) = ax² + bx + c is positive, the parabola opens upwards. If 'a' is negative, it opens downwards.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax² + bx + c, where a, b, and c are constants.