| A | B | C | D | E | F | G | H | I | JKL | MN | O | P | Q | R | S | T | UV | WXYZ |
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| Algebra 2 Connections Glossary | ||||||||||||||||||
general equation |
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| If y = f(x) is a parent equation, then the general equation for that function is given by y = af(x − h) + k where (h, k) is the point corresponding to (0, 0) in the parent graph and, relative to the parent graph, the function has been: 1) vertically stretched if the absolute value of a is greater than 1; 2) vertically compressed if the absolute value of a is less than 1; and/or 3) reflected across the x‑axis if a is less than 0. (pp. 189, 207) | |
general quadratic equation for conic sections |
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The equation  , in which a and b are not both equal to zero is a general equation that could represent a parabola, an ellipse, a hyperbola, a circle, or a pair of lines depending on the values of the coefficients. This equation represents conic sections with axes parallel to the x- or y-axes. The general equation  includes conics with axes that are not parallel to the x‑ or y‑axes. (p. 593) |
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generalize |
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| Based on several specific examples describe common characteristics, patterns, or relationships and make a conjecture that can be tested on other examples. Use variables to represent a situation or relationship. (pp. 2, 26, 214) | |
generator |
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| The generator of a sequence tells what you do to each term to get the next term. Note that this is different from the function for the nth term of the sequence. The generator only tells you how to find the following term, when you already know one term. In an arithmetic sequence the generator is the common difference; in a geometric sequence it is the multiplier or common ratio. (p. 69) | |
geometric sequence |
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| A geometric sequence is a sequence that is generated by a multiplier. This means that each term of a geometric sequence can be found by multiplying the previous term by a constant. For example: 5, 15, 45… is the beginning of a geometric sequence with generator (common ratio) 3. In general a geometric sequence can be represented a, ar, ar2, ... + arn −1. (pp. 71, 79, 80, 81) | |
geometric series (sum) |
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| The sum of a geometric sequence is a geometric series, for example: 5 + 15 + 45 + … The sum of the first n terms of a geometric sequence, a, ar, ar2 + ar3+... + arn −1 is given by the formula below. (pp. 618, 636, 641, 647)
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graph |
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The graph of an equation is the set of points representing the coordinates that make the equation true. The direction to “graph an equation” or “draw a graph” means use graph paper, scale your axes appropriately, label key points, and plot points accurately. This is different from sketching a graph. The equation
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graphing form |
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| A form of the equation of a function or relation that clearly shows key information about the graph. For example: the graphing form for the general equation of a quadratic function (also called vertex form) is y = a(x − h)2 + k. The vertex (h, k), orientation (whether a is positive or negative) and amount of stretch or compression based on |a| > 1 or |a| < 1 can be appear in the equation. (pp. 176, 177) | |
growth factor |
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| One way to analyze how the output value in a mathematical relation changes as the input value increases. Growth can be represented by constant addition, as the slope of a linear function or the constant difference in an arithmetic sequence, or by multiplication as the base of an exponential function or the multiplier in a geometric sequence. (p. 11) | |
is graphed below. (p. 9) 