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SarahDavis PrCalc1.7

Sarah Davis Precalculus 1.1-1.7

Formula/Equation/Property NameDefinition
Distance Formula d=SqRt[(x2 - x1)^2 + (y2 - y1)^2]
Midpoint Formula (x,y) = ( (x1+x2)/2, (y1 + y2)/2 )
Slope m = (y2 - y1)/ (x2-x1) , if x1 NOT EQ x2; undefined if x1 = x2
Parallel Lines Equal Slopes (m1 = m2)
Perpendicular Lines Product of slopes is -1 (m1 * m2 = -1)
Vertical Line x = a, where "a" is a constant number
Horizontal Line y = b, where "b" is a constant number
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
GENERAL form of the equation of a LINE Ax + By + C = 0, A, B not both 0
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
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
GENERAL form of the equation of a CIRCLE x^2 + y^2 + ax +by +c = 0
Equation of the Unit Circle x^2 + y^2 = 1
Quadratic Equation ax^2 + bx + c = 0, where "a" NOT = 0
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.
Discriminant in the quadratic formula, b^2 - 4ac
Quadratic Equation has 2 REAL DISTINCT solutions the discriminant b^2 - 4ac > 0
Quadratic Equation has 1 REAL solution REPEATED the discriminant b^2 - 4ac = 0
Quadratic Equation has NO REAL solutions the discriminant b^2 - 4ac < 0
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"
Transitive Property of Inequality If a < b AND b < c, THEN a < c. If a > b AND b > c, THEN a > c.
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.
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."
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."
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."
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."
Reciprocal Property of Inequality: a > 0 (1/a) > 0
Reciprocal Property of Inequality: a < 0 (1/a) < 0
Absolute value: |u| = a, a > 0 u = -a OR u = a
Absolute value: |u| <or= a, a > 0 -a <or= u; u <or= a.
Absolute value: |u| >or= a, a > 0 u <or= -a; u >or= a.
Created by: DDavis