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Question 9(Multiple Choice Worth 1 points) (08.05 MC) Use the functions f(x) and g(x) to determine which function has the smallest zero and provide its coordinates. f(x) = 2x2 − 14x + 20 x g(x) 18 −17 19 0 20 19 21 40 22 63 f(x); (2, 0) f(x); (−5, 0) g(x); (19, 0) g(x); (−17, 0) |
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Answer» Given: f(x) = 2x2 − 14X + 20 x g(x) 18 −17 19 0 20 19 21 40 22 63 f(x); (2, 0) f(x); (−5, 0) g(x); (19, 0) g(x); (−17, 0) To find: Use the functions f(x) and g(x) to determine which function has the smallest zero and provide its COORDINATES. Solution: From given, we have, x g(x) difference of g(x) difference 18 −17 19 0 0 - (-17) = 17 20 19 19 - 0 = 19 19 - 17 = 2 21 40 40 - 19 =21 21 - 19 = 2 22 63 63 - 40 =23 23 - 21 = 2
Thus g(x) is a QUADRATIC function and the regression is given as, g(x) = x^2 - 20x + 19 The zeros of g(x) are given by, x = ±√[(-20)² - 4(1)(19)]/2(1) x = ±9 The coordinates of zeros are (-9, 0) and (9, 0) f(x) = 2x^2 − 14x + 20 The zeros of f(x) are given by, x = ±√[(-14)² - 4(2)(20)]/2(2) x = ± 1.5 The coordinates of zeros are (-1.5, 0) and (1.5, 0) The smallest zero is (-1.5, 0) and it corresponds to f(x). |
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