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Algebra 2 Connections Glossary
eccentricity  
  The eccentricity of an ellipse is a measurement reflecting its “roundness. The eccentricity, e, is found with the formula pic, where c2 = a2 − b2, and a and b are the lengths of the semi-major and semi-minor axes.  For a hyperbola, the eccentricity is a measure of the shape of the curve; the larger the eccentricity the more quickly the branches spread apart.  The formula is also pic.  Note that since  c > a, the eccentricity of a hyperbola is always greater than 1; ellipses have eccentricity less than 1.  Parabolas have eccentricity equal to 1, and circles have eccentricity equal to 0.  (pp. 576, 585)
elimination to solve a system of equations 
  The key step in the elimination method of solving equations is to add or subtract both sides of the equations to eliminate one of the variables.  For example in the equations below, the variable, y, is eliminated when the two equations are added to get 13x = −13  .  (p. 66) pic
ellipse  
  The set of all points for which the sum of their distances from two fixed points, the foci, remains constant.  You can visualize an ellipse as a circle that has been stretched vertically or horizontally.  The general form of the equation of an ellipse (with a horizontal major axis) is pic.  The line through the two vertices of the ellipse in the long direction is called the major axis of the ellipse, and the distance from the center of the ellipse to one end of the major axis is called the semi‑major axis.  The shortest length across the center of the ellipse is the minor axis, and half this length is the semi-minor axis.  If a is the length of the semi-major axis, b  the semi minor axis, c  the distance from the center to either focus, and (h, k)  is the center, then the equation of the ellipse can be written
pic
           pic,  if the major axis is horizontal or
           pic,  if the major axis is vertical.

In either case, b is defined by c2 = a2 − b2, and the eccentricity is pic.  (pp. 570, 571, 575, 576)
equally likely 
 

Outcomes or events are considered to be equally likely when they have the same probability.  (pp. 497, 502, 510)

equation   
  A mathematical sentence in which two expressions have an equal sign between them. (linear pp. 11, 173, exponential p. 123, quadratic p. 177, square root p. 154)
equidistant   
  The same distance or length.  For example, all the points on a circle are equidistant from its center and that distance is the length of the radius.  (p. 566)
equilateral   
  A polygon is equilateral if all its sides have equal length.  The example at right is an equilateral hexagon. pic
equivalent   
  Two algebraic expressions are equivalent if they have the same value for any legitimate substitution for their variables.  Two equations are equivalent if they have the same solutions.  (pp. 94, 98, 119)
evaluate   
  To evaluate an expression with variables, substitute the value(s) given for the variable(s) and perform the operations according the order of operations.  For example, to evaluate the expression x3 − x2 for x = − 3  , substitute –3 for x, (− 3)3 − (−3)2 = − 27 − 9 = − 36.
event  
  Used in relation to calculating probabilities, an event is a set of outcomes or an outcome of some action that has alternative possibilities. (pp. 510, 515)
expected value   
  The expected value for an outcome is the product of the probability of the outcome and the value placed on that outcome.  The expected value of an event is the sum of the expected values for its possible outcomes. For example, in a lottery where 7 numbers are drawn from 77 and you have to have chosen all seven to win, the probability that your ticket is  the  $1,000,000 winner is pic and the expected value is $0.000416.  (pp. 497, 499, 510)
experimental probability  
  A data-based probability arrived at by conducting trials and recording the results.  When a die is rolled 20 times the experimental probability of getting a 6 is the number of times 6 comes up over the total number or rolls 20.  (p. 537)
pic
exponential function   
  An exponential function has an equation of the form y = abx for the domain of all real numbers and range positive real numbers , where a is the initial value and b is the multiplier or base.  The general form for an exponential function is f(x) = abx + 6 + k.  An example of an exponential function is graphed at right.  (pp. 55, 125, 151)
expression  
  An algebraic representation that contains one or more numbers and/or variables and may include operations and grouping symbols.  Some examples of algebraic expressions are x5 − 4x2 + 8, pic, pic, x.  (pp. 101, 102, 103
extraneous solution  
  Sometimes in the process of solving equations, multiplying or squaring expressions involving a variable will lead to a numerical result that does not make the original equation true.  This false result is called an extraneous solution.  For example, in the process of solving the equation pic both sides of the equation are squared to get x + 3 = x2 − 19x + 81 which has solutions 6 and 13.  6 is a solution of the original equation, but 13 is extraneous, because pic.  (pp. 224, 360)