INTERMEDIATE ALGEBRA
TEST CHAPTER 8 AND 9
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I.
II.
III.
In problems 1 – 3, solve the quadratic equations and simplify your answers. Use ị notation for any
imaginary numbers.
2
1.
x
3.
3x
- 8x = 17
2
2.
x2 x
- =3
3 3
+ 8x + 3 = 2
In problems 4 – 6,solve the equations using the square root property.
2
= 14
2
4.
2x
5.
x = -64
7.
Find the distance between (8,4) and (-4, -1).
(4x – 3)
6.
2
= 36
In problems 8 – 13, graph. Show on the circle—the radius and the center; the parabola—vertex
direction of the opening, axis of symmetry, the y-intercepts and/or the x-intercepts, length of the
latus rectrum ; the ellipse—the center, vertices; the hyperbola—the center, is it horizontal or
vertical, vertices, and asymptotes.
8.
y = -½(x + 2)
10.
16x
12.
(x – 3)
2
2
-3
2
- 4y = 64
2
+ (y + 5)
2
=8
2
+y
2
9.
x
= 25
11.
( x  2) 2 ( y  3) 2
+
=1
25
16
13.
y = (x – 3)
2
-7
IV.
Determine the nature of each of the following quadratic equations. Do not solve the equation.
Find the discriminate in each case and determine whether equation has (a) one rational solution,
(b) two rational solutions, (c) two irrational solutions, or (d) two nonreal complex solutions.
14.
2x
16.
3x
2
2
2
+ 5x – 3 = 0
15.
4x
-7x - 12 = 0
17.
25x
- 6x + 5 = 0
2
- 20 + 4 = 0