Academic Recovery #1/Final Exam Review Algebra C&C Units 1-4

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form f(x) = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

Front

How can you identify a quadratic function from a set of data points?

Back

A quadratic function can be identified if the data points form a parabolic shape when graphed, indicating that the relationship between the variables is not linear.

Front

What is the vertex form of a quadratic function?

Back

The vertex form of a quadratic function is f(x) = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.

Front

What does the vertex of a parabola represent in a quadratic function?

Back

The vertex represents the maximum or minimum point of the quadratic function, depending on the direction of the parabola.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are constants.

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (b^2 - 4ac) determines the nature of the roots of the quadratic equation: if positive, there are two real roots; if zero, one real root; if negative, no real roots.

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

How do you find the nth term of an arithmetic sequence?

Back

The nth term of an arithmetic sequence can be found using the formula a_n = a_1 + (n - 1)d, where a_1 is the first term and d is the common difference.

Front

What is a recursive formula?

Back

A recursive formula defines each term of a sequence using the preceding term(s). For example, in an arithmetic sequence, a_n = a_{n-1} + d.

Front

What is the difference between a linear function and a quadratic function?

Back

A linear function has a constant rate of change and graphs as a straight line, while a quadratic function has a variable rate of change and graphs as a parabola.