# Directions: Show all work and reasoning to receive full credit. ```College Algebra
Unit 2 Take Home Quiz
Due: Odd Classes October 13th
Even Classes October 14th
Name
Directions: Show all work and reasoning to receive full credit.
1) Using the Pythagorean Theorem, determine whether or not the points are the vertices of a right triangle:
(-9, 7), (-3, 7), (-3, 15).
2) Determine the center (h, k) and radius r of the circle 4 x2  4 y 2 12 x  16 y  5  0 . Graph the function.
1
1
3) Determine the general form of the equation of the circle with endpoints of a diameter at (6, -2) and
(-4, 4).
For Questions 4 &amp; 5, determine an equation, in slope-intercept form, for the line with the given
properties.
4) Parallel to the line 4 x  3 y  3 ;
5) Perpendicular to the line 2 x  9 y  66 ;
containing the point (6, 0).
containing the point (6, -13).
6) Determine the equation, in general form, of the line in the graph illustrated below.
10
8
6
(5,5)
4
(5,1)
2
-10 -8
-6
-4
-2
2
4
6
8
10
-2
-4
-6
-8
-10
For Questions 7 &amp; 8, determine the domain of the functions. Answers should be in interval notation.
x4
7) h( x)  3
8) g ( x)  3  7 x
x  4x
9) Determine and simplify the difference quotient f,
f ( x  h)  f ( x )
, h  0 , given f ( x)  2 x2  9 x  5 .
h
3x  6
x2  4
5
a) If f (x)  , what is x? What point(s) are on the graph?
3


b) List the x-intercepts and y-intercept, if any, of the graph of f.
11) Answer the following questions about the given functions, 𝑓(𝑥) = 2𝑥 + 2 and 𝑔(𝑥) = 2𝑥 2 − 2.
a) f + g
b) f – g
c) 𝑓 ∙ 𝑔
d)
𝑓
𝑔
e) f(x + 3)
12) Write an equation in general form for the circle with a radius = √7 and center = (3, -4).
13) Find all points (x, y) with the y coordinate of -3 that are 3√5 units from (5, 2).
14) Determine the other endpoint of a segment whose midpoint is (4, -2) and has one endpoint at (-7, 3).
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