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)).

Tags

CCSS.HSF-IF.C.7A

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.

Tags

CCSS.HSF-IF.C.7A

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.

Tags

CCSS.HSF-IF.C.7A

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.

Tags

CCSS.HSF-IF.C.7A

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.