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 a parabola?

Back

A parabola is the U-shaped graph of a 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

How do you find the vertex of a quadratic function?

Back

The vertex can be found using the formula (h, k), where h = -b/(2a) and k = f(h).

Front

What is the y-intercept of a quadratic function?

Back

The y-intercept is the point where the graph intersects the y-axis, found by evaluating f(0).

Front

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

Back

The range is [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 (-∞, k] where k is the y-coordinate of the vertex.

Front

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

Back

If the leading coefficient (a) is positive, the parabola opens upwards; if it is negative, it opens downwards.

Front

What is the significance of the vertex in a quadratic function?

Back

The vertex represents the maximum or minimum point of the parabola, depending on its orientation.