STAAR ALGEBRA REVIEW 2019 Flashcard 3

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has the form f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

How do you find the slope of a line given two points?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.

Front

What is the point-slope form of a linear equation?

Back

The point-slope form is given by f(x) - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

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.

Front

What does the graph of a quadratic function look like?

Back

The graph of a quadratic function is a parabola, which opens upwards if a > 0 and downwards if a < 0.

Front

How do you find the zeros of a quadratic function?

Back

The zeros can be found by solving the equation ax^2 + bx + c = 0 using factoring, completing the square, or the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a).

Front

What is the quadratic formula?

Back

The quadratic formula is used to find the solutions (or roots) of a quadratic equation and is given by x = (-b ± √(b² - 4ac)) / (2a).

Front

What is the difference between exponential and linear functions?

Back

Linear functions have a constant rate of change, while exponential functions have a variable rate of change that increases or decreases multiplicatively.

Front

What is the general form of an exponential function?

Back

The general form of an exponential function is f(x) = a * b^x, where a is a constant, b is the base, and x is the exponent.

Front

How do you determine if a function is exponential from a table of values?

Back

If the ratio of consecutive outputs (y-values) is constant, the function is exponential.