Characteristics of Quadratic Functions

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 parabola?

Back

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

Front

What does the y-intercept represent in a quadratic function?

Back

The y-intercept is the point where the graph intersects the y-axis, represented as (0, f(0)).

Front

How do you find the y-intercept of a quadratic function?

Back

To find the y-intercept, substitute x = 0 into the quadratic function.

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 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.

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.

Front

What is a parabola?

Back

A parabola is the U-shaped graph of a quadratic function.

Front

What is the domain of a quadratic function?

Back

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