Quadratics Domain and Range

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form y = ax² + bx + c, where a, b, and c are constants.

Front

What does the graph of a quadratic function look like?

Back

The graph of a quadratic function is a parabola, which can open upwards or downwards depending on the sign of the coefficient 'a'.

Front

What is the vertex of a parabola?

Back

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

Front

How do you determine if a parabola opens up or down?

Back

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

Front

What is the maximum value of a quadratic function?

Back

The maximum value occurs at the vertex of the parabola when it opens downwards.

Front

What is the minimum value of a quadratic function?

Back

The minimum value occurs at the vertex of the parabola when it opens upwards.

Front

What is the domain of a quadratic function?

Back

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

Front

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

Back

The range is from the vertex's y-coordinate to positive infinity, expressed as [k, ∞) where k is the y-coordinate of the vertex.

Front

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

Back

The range is from negative infinity to the vertex's y-coordinate, expressed as (-∞, k] where k is the y-coordinate of the vertex.

Front

What is the standard form of a quadratic function?

Back

The standard form is y = ax² + bx + c.