Quadratic Functions Vocabulary / 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 term 'vertex' refer to in a quadratic function?

Back

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

Front

How do you determine the direction a quadratic function opens?

Back

The direction is determined by the coefficient 'a' in the quadratic equation: if 'a' is positive, it opens upwards; if 'a' is negative, it opens 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 formula x = -b/(2a).

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 the set of all y-values starting 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 the set of all y-values from negative infinity to the vertex's y-coordinate, expressed as (-∞, k] where k is the y-coordinate of the vertex.

Front

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

Back

The x-intercepts can be found by setting y = 0 and solving the quadratic equation for x.

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (b² - 4ac) determines the nature of the roots: if positive, there are two real roots; if zero, one real root; if negative, no real roots.

Front

What is a parabola?

Back

A parabola is the graph of a quadratic function, characterized by its U-shape.