MATH 1100Y Quiz: MATH1100Y-Quiz-Solutions (3)
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Mathematics 1100y calculus i: calculus of one variable. [10 minutes: suppose the graph of y = x2 is stretched vertically by a factor of 3, and then shifted by 2 units to the right and 1 unit down. Find the formula of the parabola with this curve as its graph. [5: use the limit laws to evaluate lim x 0 x2 1 x2 + 1. To stretch the graph of y = x2 vertically by a factor of 3, we simply multiply the output by 3 to get y = 3x2. Shifting the graph by 2 units to the right corresponds to replacing x by x 2 to get y = 3(x 2)2. To shift the graph down by 1, we just subtract 1 to get y = 3(x 2)2 1. It follows that the formula of the desired parabola is y = 3(x 2)2 1 = 3x2 12x + 11. (cid:4)
