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 is the highest or lowest point of the parabola represented by the quadratic function, depending on whether it opens upwards or downwards.

Front

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

Back

To find the x-intercepts, set f(x) = 0 and solve the equation ax² + bx + c = 0.

Tags

CCSS.HSA-SSE.B.3B

CCSS.HSF-IF.C.8A

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 [k, ∞) where k is the y-coordinate of the vertex.

Tags

CCSS.HSF-IF.C.7A

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

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

Back

A quadratic function is increasing on the interval to the right of the vertex if it opens upwards.

Tags

CCSS.HSF-IF.C.7A

Front

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

Back

A quadratic function is decreasing on the interval to the left of the vertex if it opens upwards.

Tags

CCSS.HSF-IF.C.7A

Front

What is the maximum value of a quadratic function that opens downwards?

Back

The maximum value is the y-coordinate of the vertex.