Parabolas, 660, 661–675. See also Quadratic functions
axis of symmetry of, 319
equation of, 662–666
general equation of, 667–668
geometric definition of, 662
graphing, 663–665, 668–669
minimum/maximum values of, 319, 322
reflecting property of, 670–671
standard equation of, 663
translations of, 667–670
vertex of, 319, 322
Parallel circuits, 539
Parallel lines, 205–206
Parallel property of resistors, 539
Partial fraction(s), 540
Partial-fraction decomposition, 539–550
with distinct irreducible quadratic factors, 545
with only distinct linear factors, 540–541
with repeated irreducible quadratic factors, 546–548
with repeated linear factors, 543–544
Pascal, Blaise, 759, 760
Pascal’s Triangle, 759, 760–761
Perfect squares, factoring by making, 47
Perfect-square trinomials, 109
Perga, Apollonius of, 659
Permutations, 769–771
Perpendicular lines, 205–206
Petroleum consumption, 359–360
Pharmacokinetics, 215, 225–226
Photographs, counting arrangements for, 769–770
pH scale, 488–490
Piecewise functions, 252–256
Pitch, musical, 495–496
Pizza toppings, choosing, 773
Points
corner, of the solution set of a system of inequalities, 563
distance between, finding, 10–11, 178–179
on a graph, 222
plotting, 186–187
symmetry about, 188
turning, 341–342
writing a piecewise function from the set of, 254–255
Point-slope form, 200–201
Poiseuille, Jean Louis Marie, 263
Polygons, transformed, area of, 643–644
Polynomial(s), 30–40
adding and subtracting, 32–33
completely factored, 42
complex, 377
dividing. See Division of polynomials
factoring. See Factoring polynomials; Factoring trinomials
Factorization Theorem for Polynomials and, 377
factors of, 352
Factor Theorem and, 358–359
irreducible, 42, 44
multiplying, 33–38
in one variable, 31
Remainder Theorem and, 357–358
special products and, 34–35
in standard form, 31
Polynomial functions, 332–351
end behavior of, 335–337
graphing, 342–345, 371–372
power, 334–335
real zeros of. See Real zeros of a polynomial function
turning points of, 339–342
zeros of, 337–342
Positive numbers,
Power(s)
binomial, expanding using Binomial Theorem, 762
binomial, expanding using Pascal’s Triangle, 761
direct variation with, 405–406
Power functions, 334–335
Power growth model, 500
Power-of-a-power rule for exponents, 23, 27
Power-of-a-product rule for exponents, 23–24, 27
Power-of-quotient rules for exponents, 24, 27
Price-supply function, 227
Principal, 94, 430
Principal square root, 61
Prizewinners, counting, 1048
Probability(ies), 778–788
additive rule and, 781–782
of an event, 778–788
complements of events and, 783–784
experimental, 784–785
mutually exclusive events and, 782–783
theory of, 759
Product(s). See also Multiplication
of functions, 282
scalar, of matrices, 608
special, 34–35, 37
of sum and difference of terms, 36–38
of the sum and difference of terms, 36–38
Product rule for exponents, 21–22, 27
Product rule for logarithms, solving logarithmic equations using, 480–481
Profit function, 227
Programming, 570
Proper expressions, 353
Proportionality, constant of, 404
Ptolemy, 497
Pure imaginary numbers, 120
Pythagorean Theorem, 178