NY Regents Algebra I key terms

Any number that can be written as a fraction of two integers, with a nonzero denominator. Its decimal form either ends or repeats in a fixed block of digits.

A real number that cannot be written as a fraction of two integers. Its decimal form never ends and never repeats, such as the square root of 2 or pi.

A whole number from the set of positive counting numbers, their negatives, and zero. Integers contain no fractional or decimal part.

The distance of a number from zero on the number line, always zero or positive. Written with two vertical bars around the number.

A value that produces a given number when multiplied by itself. Every positive number has two square roots, one positive and one negative.

A number that equals an integer multiplied by itself, such as 1, 4, 9, 16, 25, or 36. Its square root is a whole number.

Shortcuts for combining powers with the same base: add exponents when multiplying, subtract when dividing, and multiply exponents when raising a power to a power.

A way to write very large or very small numbers as a number between 1 and 10 multiplied by a power of 10, such as 3.2 times 10 to the fifth.

An expression made of terms in which variables have only whole-number exponents, combined by addition or subtraction. Examples include 3x squared minus 5x plus 2.

A single term formed by a number, a variable, or their product, such as 7, x, or negative 4x squared y. It has no addition or subtraction inside it.

The largest exponent on the variable in a polynomial written in one variable. It tells the greatest number of solutions the related equation can have.

Rewriting an expression as a product of simpler expressions. Common patterns include greatest common factor, difference of squares, and trinomials that multiply back to the original.

The largest factor shared by every term in an expression. Pulling it out first often makes the remaining expression easier to factor further.

An equation whose highest power of the variable is two, usually written as a x squared plus b x plus c equals zero. It can have zero, one, or two real solutions.

A rule that solves any quadratic equation by substituting its coefficients into negative b plus or minus the square root of b squared minus 4ac, all divided by 2a.

The part of the quadratic formula under the square root, b squared minus 4ac. Its sign shows whether the equation has two, one, or no real solutions.

A method of rewriting a quadratic expression as a perfect square plus a constant. It is used to solve equations and to find the vertex of a parabola.

If the product of two factors equals zero, then at least one factor must equal zero. This lets you split a factored equation into simpler equations to solve.

Two or more equations that must be true at the same time. A solution is an ordered pair or set of values that satisfies every equation in the system.

A way to solve a system by solving one equation for a variable and replacing that variable in the other equation with the resulting expression.

A way to solve a system by adding or subtracting the equations, sometimes after multiplying one by a constant, so that one variable cancels out.

A statement comparing two linear expressions with less than, greater than, or their or-equal forms. Its solutions form a range, often shown on a number line.

Two inequalities joined by the word and or the word or. An and statement requires both conditions; an or statement requires at least one.

An equation containing an absolute value expression. Because absolute value measures distance, it usually splits into two separate cases that must both be checked.

A rule that assigns exactly one output value to each allowed input value. Passing the vertical line test on a graph confirms the relation is a function.

The complete set of input values for which a function or relation is defined. On a graph, it is read from left to right along the horizontal axis.

The complete set of output values a function actually produces. On a graph, it is read from bottom to top along the vertical axis.

Writing a function as f of x equals an expression, where f names the rule and x is the input. It makes substituting an input and naming outputs compact.

How much the output changes for each unit change in the input, found by dividing the change in y by the change in x. For a line it equals the slope.

A function whose graph is a straight line and whose rule can be written as y equals m x plus b. It changes at a constant rate.

A function of the form y equals a times b to the x power, where b is positive and not 1. It grows or decays by a constant percent each step.

The U-shaped curve that is the graph of a quadratic function. It opens upward when the leading coefficient is positive and downward when it is negative.

A way of writing a quadratic function as y equals a times the quantity x minus h squared plus k. The point (h, k) is the vertex of the parabola.

The vertical line through a parabola's vertex that divides the curve into mirror-image halves. Its equation is x equals the x-coordinate of the vertex.

A measure of how steep a line is, computed as rise over run or the change in y divided by the change in x. Parallel lines share a slope.

The point where a graph crosses the vertical axis, occurring where x equals zero. In y equals m x plus b, the value b is the y-intercept.

An ordered list of numbers formed by a rule. Each number is a term, and the position of a term is its index, starting with the first.

A list of numbers in which each term after the first is found by adding the same constant, called the common difference, to the previous term.

A list of numbers in which each term after the first is found by multiplying the previous term by the same constant, called the common ratio.

A change in a graph's position, size, or orientation, such as a translation, reflection, rotation, or dilation. Function rules can describe each change.

A slide that moves every point of a figure the same distance in the same direction without turning or resizing it. Adding to x shifts right; adding to y shifts up.

A transformation that enlarges or shrinks a figure by a scale factor while keeping its shape. A dilation centered at the origin multiplies coordinates by that factor.

Figures with the same shape but possibly different sizes. Their corresponding angles are equal and their corresponding side lengths share a constant ratio.

In a right triangle, the square of the hypotenuse equals the sum of the squares of the two legs. It is often used to find a missing distance.

A rule giving the distance between two points by taking the square root of the sum of the squared differences of their x-coordinates and y-coordinates.

A rule giving the point exactly halfway between two points by averaging their x-coordinates and averaging their y-coordinates separately.

The sum of all data values divided by the number of values. It is affected strongly by unusually large or small values in a data set.

The middle value of a data set arranged in order. If there is an even number of values, it is the mean of the two middle values.

A measure of how spread out data values are around the mean. A larger value means the data are more scattered; a smaller value means they cluster.

A value that divides ordered data into four groups of roughly equal size. The first quartile is the median of the lower half; the third is the median of the upper half.

The difference between the third quartile and the first quartile. It describes the spread of the middle half of the data and resists the pull of outliers.

A data value far from the rest of the set. In a box plot it is often plotted separately because it can distort the mean and range.

A straight line drawn through a scatter plot that comes closest to the plotted points. It is used to describe a trend and make predictions.

A number between negative 1 and 1 that measures how closely two variables follow a straight-line pattern. A value of zero means no linear trend.

A bell-shaped pattern in which data cluster near the mean and thin out symmetrically toward the extremes. About 68 percent of values lie within one standard deviation of the mean.

A table that sorts data by two categories, showing counts in each combination. Row and column totals allow comparison of conditional relative frequencies.

The chance that an event happens given that another event has already happened. It is calculated by dividing a joint frequency by the frequency of the given condition.

The set of all possible outcomes of a random experiment. Listing it helps you count favorable outcomes when computing a probability.