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Unformatted text preview: Solutions to Quiz 1A
www.math.uﬂ.edu/ harringt
January 10, 2008
1. Find an equation of a line that goes through (−1, 2) 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 (−1, 2) and has m = 0. Using the slopeintercept
formula we have that
y − y1 = m(x − x1 )
y − 2 = 0(x + 1)
y=2
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 + 4x = 0.
x2 + y 2 + 4x
(x2 + 4x) + (y 2 )
42
+ y2
x2 + 4x +
2
(x + 2)2 + y 2
(x − (−2))2 + (y − 0)2 =0
=0
= 4
2 2 =4
= 22 Thus, the center is (−2, 0) and the radius is 2.
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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 Calculus, Geometry, Slope

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