This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Hapa kuna suluhisho la swali lako: a) Kamilisha jedwali Tunatumia kazi y = 2x^2 - x - 6 kukokotoa maadili ya y kwa kila thamani ya x. Kwa x = -3: y = 2(-3)^2 - (-3) - 6 = 2(9) + 3 - 6 = 18 + 3 - 6 = 15 Kwa x = -2: y = 2(-2)^2 - (-2) - 6 = 2(4) + 2 - 6 = 8 + 2 - 6 = 4 Kwa x = -1: y = 2(-1)^2 - (-1) - 6 = 2(1) + 1 - 6 = 2 + 1 - 6 = -3 Kwa x = 0: y = 2(0)^2 - (0) - 6 = 0 - 0 - 6 = -6 Kwa x = 1: y = 2(1)^2 - (1) - 6 = 2(1) - 1 - 6 = 2 - 1 - 6 = -5 Kwa x = 2: y = 2(2)^2 - (2) - 6 = 2(4) - 2 - 6 = 8 - 2 - 6 = 0 Kwa x = 3: y = 2(3)^2 - (3) - 6 = 2(9) - 3 - 6 = 18 - 3 - 6 = 9 Kwa x = 4: y = 2(4)^2 - (4) - 6 = 2(16) - 4 - 6 = 32 - 4 - 6 = 22 Jedwali lililokamilika ni: | x | -3 | -2 | -1 | 0 | 1 | 2 | 3 | 4 | |---|---|---|---|---|---|---|---|---| | y | 15 | 4 | -3 | -6 | -5 | 0 | 9 | 22 | b) Chora grafu ya y = 2x^2 - x - 6 kwa -3 x 4 Tumia pointi zifuatazo kutoka kwenye jedwali ili kuchora grafu kwenye gridi uliyopewa: (-3, 15), (-2, 4), (-1, -3), (0, -6), (1, -5), (2, 0), (3, 9), (4, 22). Unganisha pointi hizi kwa kutumia mstari laini ili kuunda parabola. c) Tumia grafu yako kutatua 2x^2 - x - 6 = 0 Kutatua 2x^2 - x - 6 = 0 kwa kutumia grafu kunamaanisha kutafuta maadili ya x ambapo y = 0. Haya ni maeneo ambapo grafu inapita kwenye mhimili wa x. Kutoka kwenye jedwali na grafu, tunaona kwamba y=0 wakati x=2. Pia, grafu inapita mhimili wa x kati ya x=-2 na x=-1. Kwa kukadiria kutoka kwenye grafu, au kwa kutatua mlinganyo, tunapata thamani nyingine. Kutatua mlinganyo 2x^2 - x - 6 = 0: (2x+3)(x-2) = 0 Hivyo, 2x+3 = 0 x = -(3)/(2) = -1.5 Au x-2 = 0 x = 2 Kwa hiyo, suluhisho kutoka kwenye grafu ni: x = -1.5 na 2 3 done, 2 left today. You're making progress.