Characteristics of Quadratic Functions (Graph #1)

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form f(x) = ax^2 + 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) = ax^2 + bx + c.

Front

What is the vertex of a quadratic function?

Back

The vertex of a quadratic function is the point (h, k) where the function reaches its maximum or minimum value, given by the formula h = -b/(2a) and k = f(h).

Front

How do you find the axis of symmetry for a quadratic function?

Back

The axis of symmetry for a quadratic function in standard form f(x) = ax^2 + bx + c is given by the line 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 of a quadratic function that opens upwards 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 of a quadratic function that opens downwards is (-∞, k], where k is the y-coordinate of the vertex.

Front

What does it mean for a quadratic function to open upwards?

Back

A quadratic function opens upwards when the coefficient a > 0, resulting in a U-shaped graph.

Front

What does it mean for a quadratic function to open downwards?

Back

A quadratic function opens downwards when the coefficient a < 0, resulting in an inverted U-shaped graph.

Front

How does the value of 'a' affect the graph of a quadratic function?

Back

The value of 'a' affects the width and direction of the parabola; larger absolute values of 'a' make the graph narrower, while smaller absolute values make it wider.