Alg 1 Final Review #1

Front

What is the average rate of change of a function f(x) on the interval [a, b]?

Back

The average rate of change of a function f(x) on the interval [a, b] is calculated using the formula: \( \frac{f(b) - f(a)}{b - a} \).

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 do you find the vertex of a quadratic function in standard form?

Back

The vertex of a quadratic function \( f(x) = ax^2 + bx + c \) can be found using the formula: \( x = -\frac{b}{2a} \).

Front

What is the vertex form of a quadratic function?

Back

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

Front

What does the discriminant of a quadratic equation tell you?

Back

The discriminant \( D = b^2 - 4ac \) indicates the nature of the roots of the quadratic equation: if D > 0, there are two distinct real roots; if D = 0, there is one real root; if D < 0, there are no real roots.

Front

What is the quadratic formula?

Back

The quadratic formula is used to find the roots of a quadratic equation \( ax^2 + bx + c = 0 \) and is given by: \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \).

Front

How do you convert a quadratic function from standard form to vertex form?

Back

To convert from standard form \( f(x) = ax^2 + bx + c \) to vertex form, complete the square.

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 the common difference in an arithmetic sequence?

Back

The common difference in an arithmetic sequence is the constant amount that each term increases or decreases by, calculated as \( d = a_{n+1} - a_n \).