A mathematical sentence in which two expressions appear on either side of an "equals" sign (=), stating that the two expressions are equivalent.
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x-intercept
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The point(s) where a graph intersects the x-axis. A graph may have several x-intercepts, no x-intercepts, or just one. We sometimes report the x-intercepts of a graph with coordinate pairs, but since the y-coordinate is always zero, we often just give the x-coordinates of x-intercepts.
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output value
Front
The output value is the dependent variable in a relation. When we substitute the input value into our rule (equation), the result is the output value. For example, if we have a rule for how much your phone bill will be if you talk a certain number of minutes, the amount of your phone bill is the output value. The output value appears second in an x → y table, and is represented by the variable y. When working with functions, the output value, an element of the range, is the value that results from applying the rule for the function to an input value.
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line of symmetry
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A line that divides a shape into two pieces that are mirror images of each other. If you fold a shape over its line of symmetry, the shapes on both sides of the line will match perfectly.
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quadratic function
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In this course, a parabola is always the graph of a quadratic function y = ax^2 + bx + c where a does not equal 0. The highest or lowest point on the graph is called the vertex.
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maximum
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As great, high, or intense as possible or permitted.
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function
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A relation in which for each input value there is one and only one output value. For example, the relation f(x) = x + 4 is a function; for each input value (x) there is exactly one output value. In terms of ordered pairs (x, y), no two ordered pairs of a function have the same first member (x).
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input value
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The input value is the independent variable in a relation. We substitute the input value into our rule (equation) to determine the output value. For example, if we have a rule for how much your phone bill will be if you talk a certain number of minutes, the number of minutes you talk is the input value. The input value appears first in an x → y table, and is represented by the variable x. When working with functions, the input value, an element of the domain, is the value put into the function.
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parabola
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A parabola is a particular kind of mathematical curve. In this course, a parabola is always the graph of a quadratic function y = ax^2 + bx + c where a does not equal 0. The diagram below shows some examples of parabolas. The highest or lowest point on the graph is called the vertex.
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minimum
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The least or smallest amount or quantity possible, attainable, or required.
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x-y table
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Represents pairs of values of two related quantities.
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absolute value
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The distance of the number from zero.
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range
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The set of all output values for a function or relation.
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graph
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A graph represents numerical information spatially. The numbers may come from a table, situation (pattern), or rule (equation or inequality). Most of the graphs in this course show points, lines, and/or curves on a two-dimensional coordinate system like the one below or on a single axis called a number line.
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y-intercept
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The point(s) where a graph intersects the y-axis. A function has at most one y-intercept; a relation may have several.
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domain
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The set of all input values for a relation or function. For example, the domain of the relation graphed below is x > −3. For variables, the domain is the set of numbers the variable may represent.
