Characteristics of Quadratics

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 and a ≠ 0.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is y = ax² + bx + c.

Front

What does the graph of a quadratic function look like?

Back

The graph of a quadratic function is a parabola, which opens upwards if a > 0 and downwards if a < 0.

Front

What is the vertex of a quadratic function?

Back

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

Front

How do you find the vertex of a quadratic function in standard form?

Back

The vertex can be found using the formula x = -b/(2a) and then substituting x back into the function to find y.

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 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 from the y-coordinate of the vertex to positive infinity, written 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 y-coordinate of the vertex, written as (-∞, k] where k is the y-coordinate of the vertex.

Front

What does it mean for a quadratic function to be increasing?

Back

A quadratic function is increasing on the interval where the y-values rise as the x-values increase.