# What are the factors of x 2 + 40y + 371

## Applying mathematics HAK 2, textbook

Functional relationships 371. a. A b. C 372. Intersection: (4 1 4) The intersection of the straight lines is the solution of the system of equations. 4 Quadratic Equations and Quadratic Functions 4.1 Quadratic Equations 415. a. ^ ļ `4 x 1, 2 = 8 ± 9 ______ 2 16 _ 2 3 2 + 225 = 8 ± 9 __ 289 = 8 ± 17, so x 1 = - 9, x 2 = 25 5 b. ^ `4 x 1, 2 = 11 ± 9 ______ 11 2 ļ ™ ™ ___ 2 · 3 = 11 ± 9 __ 61 __ 6, so x 1 = 3.135, x 2 = 0.532 5 c. ^ ļ ļ `4 Multiplying and combining leads to the equation 4x 2 + 39x + 27 = 0. x 1, 2 = ļ“ 9 _______ 39 2 ļ ™ ™ ___ 2 · 4 = ļ “9 ___ 1089 __ 8, so is x 1 ļ [2 ļ 5 416. a. 0 4 ļ 2 _ 4 x ļ 5 d. 2 4 2 2 _ 4 + 1 = 2> 0 5 b. 1 4 8 2 _ 4 - 16 = 0 5 e. 0 4 2 ļ 5 _ 2 3 2 _ 4 - 13 _ 2 ļ 79 _ 16 5 c. 2 4 ļ 2 _ 4 - 3 = 3.25> 0 5 f. 2 4 2 7 _ 3 3 2 _ 4 + 5 _ 3 = 109 _ 36> 0 5 417.4cm [Solve the equation x (x + 3 , 5) = 30, i.e. x 2 + 3.5 x - 30 = 0. 'LH / ØVXQJHQ VLQG ļ XQG' D HLQH 6HLWHQOÆQJH SRVLWLY VHLQ only 4 is possible.] 418. 1.8% pa [Solve the equation 5000 (1 + i) 2 + 8000 (1 + i) = 13325.62. The / ØVXQJHQ VLQG ļ XQG 'HU = LQVVDW] PXVV SRVLWLY VHLQ thus 1.8%.] 4.2 Quadratic functions 467. f (x) = 2 2 x - 5 _ 4 3 2 - 1 _ 8; Vertex: 2 5 _ 4 1 ļ 1 _ 8 3 4 f (x) = 2x 2 - 5x + 3 = 2 2 x 2 - 5 _ 2 x + 2 5 _ 4 3 2 3 + 3 - 2 2 5 _ 4 3 2 = 2 2 x - 5 _ 4 3 2 - 1 _ 8 5 468. The graph of f has the vertex (3 1 ļ: LU HUKDOWHQ GHQ * UDSKHQ of f, by shifting the graph of g so that the point (0 1 0) in the vertex (3 1 ļ] X OLHJHQ NRPPW 'DV KHLÁW ZLU YHUVFKLH- EHQ J XP (LQKHLWHQ HQWODQJ GHU [$ FKVH XQG XP ļ (LQKHLWHQ along the y-axis, A. 469. a. C c. A, B e. C, D g. B b. B, D d. D f. C h. A 470. a. 'DD ļ LVW KDW I HLQHQ JUØÁWHQ) XQNWLRQVZHUW b. I [ļ [x 2 + 24, therefore the vertex is (1 1 24) and f has a largest function value, therefore f has two zeros. 471. 3 + 9 _ Ň ļ 9 _ Ň> / ØVH GLH * OHLFKXQJ [2 - 3x + 1 = 0 .] 472. (2 1 0) and (3 1 0) [Solve the equation x 2 - 5x + 6 = 0.] 473. The graph of a quadratic function intersects the x-axis in either two points, touches them at one point or does not intersect.474. a. FD XQG W! RGHU D! XQG W b. CD! RGHU D c. ED! W! RGHU DW 4.3 Modeling with quadratic functions 510. f with f (x) = 0.5x 2 + 3x - 4 [Solve the system of equations I) 4a + 2b + c = 4 II) 16a + 4b + c = 16 III) 36a + 6b + c = 32 'LH / ØVXQJ LVW DEF ļ @ 511. I PLW I [ļ [x 2 E] ZI [ļ [2 + 12x - 10 [The vertex is (3 1 8) so f (x) = a · (X - 3) 2 + 8 and f (1) = 0, DOVR ID ™ XQG D ļ 'DKHU LVW I [ļ [x 2 ļ [2 + 12x - 10.] 512. a. K with K (x) = 0.1 x 2 + 4.5 x + 75 [Solve the system of equations I) 5 2 a + 5b + c = 100 II) 30 2 a + 30b + c = 300 III) 50 2 a + 50b + c = 550 The solution is a = 0.1, b = 4.5, c = 75.] b. 1075GE [K (80) = 1075] 513. a. * PLW * [ļ [2 + 1730x - 2500 [E (x) = 1980x; G (x) = E (x) - K (x) = 1980x - (32x 2 + 250x + 2500) = ļ [2 + 1730x - 2500] b. Break-even point: 2 guitars (x = 1.49), profit limit: 52 guitars (x = 52.58) [G (x) = 0 É ļ [2 + 1730x - 2500 = 0. This equation has the solutions 1.49 and 52.58.] C. If the company produces more than 52 guitars, it makes a loss. d. 27 guitars, maximum profit: 20882 € 4 * [ļ 2 x - 865 _ 32 3 2 + 668225 _ 32 w vertex (27.03 1 20882.03) 5 4.4 Polynomial functions 537. a. * UDG / HLWNRHIIL] LHQW 1XOOVWHOOHQ ļ [f (x) = 4x 4 - 20x 3 - 12x 2 + 52x + 40, the greatest power is 4, so the degree is 4, the coefficient of x 4 is 4. Zeros are the solution - according to the equation 4 (x + 1) 2 · (x - 2) · (x - 5) = 0. A product is 0 exactly if one of the factors is 0, i.e. if (x + 1) = 0, ( x - 2) = 0 or (x - 5) = 0. That is exactly then the) DOO ZHQQ [ļ [RGHU [LVW @ xy 0 4 8 4 8 I II (4 1 4) xy 0 2 3 1 -1 - 2 2 1 -1 - 2 xy 0 2 3 1 -1 - 2 2 1 -1 - 2 xy 0 2 3 4 1 -1 2 1 -1 3 xy 0 2 3 1 -1 - 2 1 -1 - 2 - 3 xy 0 2 3 4 1 -1 2 1 -1 3 xy 0 2 3 4 1 -1 1 -1 - 2 - 3 185 Answers to "What have I learned?" For testing purposes only - property of the publisher öbv

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