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

• factoring, 44

Perga, Apollonius of, 659

Permutations, 769–771

• distinguishable, 773–774

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

• graphing, 255–256

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, 7

• on number line, 6

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

• rational, 540

Proportionality, constant of, 404

Ptolemy, 497

Pure imaginary numbers, 120

Pythagorean Theorem, 178

• converse of, 179