Quadratic Functions and Sequences Worksheet

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, found at the point (h, k) in the vertex form f(x) = a(x-h)² + k.

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 first common difference (Δx)?

Back

The first common difference (Δx) is the difference between consecutive x-values in a sequence.

Front

What is the second common difference (2nd Δy)?

Back

The second common difference (2nd Δy) is the difference of the differences of the y-values in a sequence, indicating the rate of change of the first differences.

Front

What does it mean if the second differences are constant?

Back

If the second differences are constant, the sequence of y-values represents a quadratic function.

Front

How do you find the first common difference (Δx) for a set of x-values?

Back

To find the first common difference (Δx), subtract each x-value from the next one in the sequence.

Front

What is an arithmetic sequence?

Back

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant.

Front

What is a geometric sequence?

Back

A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.