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24 Cards in this Set
- Front
- Back
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Distance Formula
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Square root of [ (X2-X1) ^2 + (Y2-Y1)^2]
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Midpoint Formula
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Average of the Xs, Average of the Ys.
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Parabola Formulas
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Y=a(x-h)^2 + K
X = a(y-k)^2 + H |
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In a Parabola, the distance from the vertex to either the focus or the directrix is....
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1/(4a)
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In a Parabola, the length of the latus rectum is...
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| 1/a |
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How many points are required when you graph a parabola?
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Five
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What is the focus of a parabola?
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the main point where the parabola starts
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What is the directrix of a parabola?
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the line corresponding to the focus.
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the discriminate of a parabola formula.
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b^2 - 4ac
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What is a parabola?
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The set of all points in a plane that are equidistant from a given point and a givien line.
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The General Equation of a Circle
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(x-h)^2 + (y-k)^2 = r^2
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Fundamental Theorem of Algebra
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Every polynomial equation with degree greater than zero has at least one root in the set of complex numbers.
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Corollary about the nth degree polynomial.
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An nth degree polynomial has exactly n roots in the complex numbers.
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Complex Conjugates Theorem:
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If a + bi is a zero of a polynomial function with real coefficients, then a - bi is also a zero of the polynomial.
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Descarte' Rule of Signs:
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For a polynomial P(x) with terms arranged in descending powers
a) THe number of positive real zeros of P(x) is the same as the number of changes in sign of the coefficients of the terms, or is less than this by an even number. b) The number of negative real zeros of P(x) is the same as the number of changes in sign of the coefficients of the terms of P(-x), or is less than this by an even number. |
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Rational Root Theorem:
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The possible rational roots of a polynomial are numbers of the form p/q or -p/q , where p is a factor of the constant and q is a factor of the leading coefficient.
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What are Inverse Functions
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Two functions f and g are called inverse functions if and only if their compositions are the identity function. That is, f(g(x))=x and g(f(x))=x
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Exponential Function
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a function of the form f(x) = a ^x, where a is a positive number not equal to 1
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Common Logarithms
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Logs with base 10. Often, the when the ten is ignored, we assume that it is base 10.
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e= what?
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2.71
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A sequence is...
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a list of numbers, separated by commas
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An arithmetic sequence is
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when the numbers increase (or decrease) by addition
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A geometric sequence is
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when the numbers increase (or decrease) by multiplication
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A series is
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the sum of the terms of a sequence
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