Key Features of Quadratic Functions

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically written 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 where the graph changes direction, representing either the maximum or minimum value of the function.

Front

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

Back

The y-intercept of a quadratic function can be found by evaluating the function at x = 0, which gives the point (0, f(0)).

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 significance of the ordered pair (0, c) in a quadratic function?

Back

The ordered pair (0, c) represents the y-intercept of the graph, where the graph crosses the y-axis.

Front

What does the range of a quadratic function indicate?

Back

The range of a quadratic function indicates the set of possible output values (y-values) that the function can produce.

Front

What is the maximum or minimum value of a quadratic function?

Back

The maximum or minimum value of a quadratic function occurs at the vertex, depending on the direction of the parabola (opening upwards or downwards).

Front

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

Back

A quadratic function opens upwards if the leading coefficient (a) is positive and downwards if it is negative.

Front

What is the significance of the ordered pair (h, k) in vertex form?

Back

In vertex form, f(x) = a(x - h)^2 + k, the ordered pair (h, k) represents the vertex of the parabola.