Stitz-Zeager_College_Algebra_e-book

74 as a guide show that the function g whose graph is

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Unformatted text preview: = (x − 3)2 . Its distance to the origin, (0, 0), is given by d= (x − 0)2 + (y − 0)2 = x2 + y 2 = x2 + [(x − 3)2 ]2 = x2 + (x − 3)4 Since y = (x − 3)2 Given a value for x, the formula d = x2 + (x − 3)4 is the distance from (0, 0) to the point (x, y ) on the curve y = (x − 3)2 . What we have defined, then, is a function d(x) which we wish to minimize over all values of x. To accomplish this task analytically would require Calculus so as we’ve mentioned before, we can use a graphing calculator to find an approximate solution. Using the calculator, we enter the function d(x) as shown below and graph. Using the Minimum feature, we see above on the right that the (absolute) minimum occurs near x = 2. Rounding to two decimal places, we get that the minimum distance occurs when x = 2.00. To find the y value on the parabola associated with x = 2.00, we substitute 2.00 into the equation to get y = (x − 3)2 = (2.00 − 3)2 = 1.00. So, our final answer is (2.00, 1.00).15 (What does the y v...
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This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

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