Sarah Davis Precalculus 1.1-1.7
Quiz yourself by thinking what should be in
each of the black spaces below before clicking
on it to display the answer.
Help!
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| Distance Formula | d=SqRt[(x2 - x1)^2 + (y2 - y1)^2]
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| Midpoint Formula | (x,y) = ( (x1+x2)/2, (y1 + y2)/2 )
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| Slope | m = (y2 - y1)/ (x2-x1) , if x1 NOT EQ x2; undefined if x1 = x2
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| Parallel Lines | Equal Slopes (m1 = m2)
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| Perpendicular Lines | Product of slopes is -1 (m1 * m2 = -1)
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| Vertical Line | x = a, where "a" is a constant number
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| Horizontal Line | y = b, where "b" is a constant number
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| Point-Slope form of the equation of a line | y - y1 = m(x - x1); "m" is the slope of the line, (x1, y1) are the coordinates of the point on the line
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| GENERAL form of the equation of a LINE | Ax + By + C = 0, A, B not both 0
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| Point-Slope-Intercept form of the equation of a line | y = mx + b; "m" is the slope of the line, "b" is the y-intercept
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| STANDARD form of the equation of a CIRCLE | (x - h)^2 + (y - k)^2 = r^2; "r" is the radius of the circle, (h,k) are the coordinates of the center of the circle
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| GENERAL form of the equation of a CIRCLE | x^2 + y^2 + ax +by +c = 0
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| Equation of the Unit Circle | x^2 + y^2 = 1
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| Quadratic Equation | ax^2 + bx + c = 0, where "a" NOT = 0
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| Quadratic FORMULA | x = [-b plus or minus SqRt(b^2 - 4ac)] /(2a) AND (b^2 - 4ac) NOT negative; in the quadratic equation "a" is the coefficient of x^2, "b" the coefficient of x, and "c" is the pure numerical term.
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| Discriminant | in the quadratic formula, b^2 - 4ac
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| Quadratic Equation has 2 REAL DISTINCT solutions | the discriminant b^2 - 4ac > 0
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| Quadratic Equation has 1 REAL solution REPEATED | the discriminant b^2 - 4ac = 0
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| Quadratic Equation has NO REAL solutions | the discriminant b^2 - 4ac < 0
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| Trichotomy Inequality Property | a < b or a = b or b < a
"2 numbers are related to each other by one of the above 3 ways"
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| Transitive Property of Inequality | If a < b AND b < c, THEN a < c. If a > b AND b > c, THEN a > c.
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| Addition Property of Inequality | If a < b, THEN a + c < b + c. "If a first quantity is less than a second quantity, the same amount can be added to both quantities, and the new first quantity will still be less thant the new second quantity." If a > b, then a + c > b + c.
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| Multiplication Property of Inequality: 2 quantities (a < b) multiplied by the same positive number | If a < b and if c > 0, then ac < bc. "The resulting new first quantity is still less than the resulting new second quantity."
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| Multiplication Property of Inequality : 2 quantities (a < b) mulitplied by the same NEGATIVE number | If a < b and if c < 0, then ac > bc "The resulting new first quantity is then GREATER than the resulting new second quantity."
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| Multiplication Property of Inequality: 2 quantities (a > b) multiplied by the same positive number | If a > b and if c > 0, then ac > bc. "The resulting new first quantity is still greater than the resulting new second quantity."
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| Multiplication Property of Inequality : 2 quantities (a > b) mulitplied by the same NEGATIVE number | If a > b and if c < 0, then ac < bc "The resulting new first quantity is then LESS than the resulting new second quantity."
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| Reciprocal Property of Inequality: a > 0 | (1/a) > 0
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| Reciprocal Property of Inequality: a < 0 | (1/a) < 0
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| Absolute value: |u| = a, a > 0 | u = -a OR u = a
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| Absolute value: |u| <or= a, a > 0 | -a <or= u; u <or= a.
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| Absolute value: |u| >or= a, a > 0 | u <or= -a; u >or= a.
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Created by:
DDavis
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