quiz1Bsol - Solutions to Quiz 1B www.math.ufl.edu/...

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Unformatted text preview: Solutions to Quiz 1B www.math.ufl.edu/ harringt January 10, 2008 1. Find an equation of a line that goes through (2, −1) and is parallel to the x-axis. First we note that the x-axis has zero slope. So we want to find a line that goes through (2, −1) and has m = 0. Using the slope-intercept formula we have that y − y1 = m(x − x1 ) y + 1 = 0(x − 2) y = −1 NOTE: Some people might have found it easier to simply graph the point and the x-axis to find the equation. 2. Find the center and radius of x2 + y 2 + 6x = 0. x2 + y 2 + 6x (x2 + 6x) + (y 2 ) 62 + y2 x2 + 6x + 2 (x + 3)2 + y 2 (x − (−3))2 + (y − 0)2 =0 =0 = 6 2 2 =9 = 32 Thus, the center is (−3, 0) and the radius is 3. 3. Solve the inequality in terms of intervals: x3 − x ≥ 0 First we will factor, so we have that x(x − 1)(x + 1) ≥ 0. Next we will use a sign chart. (You may also use a table.) 1 x x-1 x+1 f(x) - --0+ 0+ -1 0 + 0 0 +++ -0+ +++ -0+ 1 We are looking for the + and 0 in the sign chart since x3 − x ≥ 0. So the interval is [−1, 0] ∪ [1, ∞). 2 ...
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quiz1Bsol - Solutions to Quiz 1B www.math.ufl.edu/...

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