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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 xaxis.
First we note that the xaxis has zero slope. So we want to ﬁnd a line
that goes through (2, −1) and has m = 0. Using the slopeintercept
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 xaxis 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
x1
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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 Fall '08
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 Calculus, Geometry, Slope

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