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 quadratic function?

Back

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

Front

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

Back

To find the x-intercepts, set the quadratic function equal to zero and solve for x.

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 domain of a quadratic function?

Back

The domain of a quadratic function is all real numbers, expressed as (-∞, ∞).

Front

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

Back

A quadratic function is increasing on the interval to the right of the vertex and decreasing on the interval to the left of the vertex.

Front

What are the characteristics of the graph of a quadratic function?

Back

The graph of a quadratic function is a parabola that can open upwards or downwards, has a vertex, an axis of symmetry, and may have x-intercepts.

Front

What is the significance of the coefficients a, b, and c in a quadratic function?

Back

The coefficient 'a' determines the direction and width of the parabola, 'b' affects the position of the vertex, and 'c' represents the y-intercept.