1/2-Part A - Algebra 1: Connection and Concepts Pre-Assessments

Front

What is the average rate of change of a function between two points?

Back

The average rate of change of a function between two points (x1, y1) and (x2, y2) is calculated as \( \frac{y2 - y1}{x2 - x1} \).

Front

Define 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

What is the formula for the average rate of change of a quadratic function?

Back

The average rate of change of a quadratic function between two points \( x_1 \) and \( x_2 \) is given by \( \frac{f(x_2) - f(x_1)}{x_2 - x_1} \).

Front

How do you find the difference of two functions, P(x) and Q(x)?

Back

To find the difference of two functions, subtract the second function from the first: \( P(x) - Q(x) \).

Front

What is the expression for the total area of two rectangles given by (x)(3x + 1) + (2x)(x + 3)?

Back

The total area can be simplified to \( 5x^2 + 7x \).

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 is the constant amount that each term increases or decreases by in an arithmetic sequence.

Front

What is the formula for a linear function?

Back

A linear function can be expressed in the form \( f(x) = mx + b \), where m is the slope and b is the y-intercept.

Front

How do you model data using a function?

Back

To model data using a function, identify the relationship between the variables and choose a function type (linear, quadratic, etc.) that best fits the data.