# Algebra 2

Find the distance between the points (12, 8) and (4, 2).
100 units
14 units
10 units
–10 units

Find the midpoint of the points (3, 1) and (7, –5).
(1, 6)
(2, 1)
(2, –3)
(5, –2)

Find the vertex and focus of the parabola whose equation is 4y = x2 + 4.
V(0, 4), F(0, 3)
V(0, 1), F(0, 2)
V(4, 0), F(3, 0)
V(1, 0), F(2, 0)

Find the center and radius of the circle whose equation is x2 + 10x + y2 = 75.
C(–10, 0), r = 100
C(–10, 0), r = 10
C(–5, 0), r = 100
C(–5, 0), r = 10

Identify the type of equation presented in x2 + y2 – 4x + 12y – 6 = 0.
parabola
circle
ellipse
hyperbola

Solve the following system of equations.
x2 + y2 = 64
x2 + 64y2 = 64
(8, 0), (–8, 0)
(0, 8), (0, –8)
(8, 0)
(0, –8)

Find f(–2) for f(x) = –x3 – 2x2 + 7x + 1.
–1
–6
–13
–29

Identify the factors of the polynomial x3 + x2 – 14x – 24.
(x – 2)(x + 2)(x + 6)
(x + 2)(x + 3)(x – 4)
(x + 1)(x – 3)(x + 8)
(x – 1)(x + 4)(x + 6)

Identify all rational zeros of the polynomial function f(x) = x3 + 2x2 – 5x – 6.
–1, 2, –3
–1, –2, 3
1, –2, –3
1, 2, 3

Identify all zeros of the polynomial function f(x) = x4 – 9x3 + 24x2 – 6x – 40.
–2, 4, 1 – i, 1 + i
–2, 4, 2 – i, 2 + i
–1, 4, 2 – i, 2 + i
–1, 4, 3 – i, 3 + i

Find f(g(–2)) if f(x) = 4x + 5 and g(x) = x2 – 1.
8
17
12
21

Identify the inverse of the function f(x) = –7x + 2.

If y varies inversely with x, and y = 6 when x = 18, find y when x = 8.
13 ½
2 ⅔
12
24

If y varies jointly as x and z, and y = 60 when x = 10 and z = –3, find y when x = 8 and z = 15.
–240
–120
–15
–9.6

Chase can do a job in 4 hours, while Campbell can do the same job in 2 hours. How long will it take the two of them to do the job together?
6 hours
3 hours
2 ⅔ hours
1 ⅓ hours

Solve the equation 4(x + 2) = 8(x – 1).
4
5
7
8

Solve the equation log8 (x2 + 4x) = log8 12.
2
6
–2, 6
2, –6

Solve the equation log2 3 = log2 (7x – 8) – log2 x.
no solution
1
2
4

Find the antilogarithm of 1.7.
.2304
.5306
5.47
50.12

Solve the equation ln x = 2. Round the answer to four decimal places.
7.3891
.3010
.6931
100

Solve the equation 8(x – 2) = 5x. Round the answer to three decimal places.
9.578
8.850
5.293
6.147

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1. We do not do your work for you. Once you have attempted to answer your questions, we will be happy to give you feedback on your work. Although it might require more time and effort, you will learn more if you do your own work. Isn't that why you go to school?

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2. 1. (12,8), (4,2).
d^2 = (4-12)^2 + (2-8)^2 = 100,
d = 10.

2. (3,1), (7,-5).
Xo = (3+7) / 2 = 5.
Yo = (1-5) / 2 = -2.
M((Xo,Yo),
M(5,-2).

3. 4Y = X^2 + 4.
Divide both sides by 4:
Y = (1/4)X^2 + 1,

h = Xv = -b/2a = -0 / (1/2) = 0.

k = Yv = (1/4)0^2 + 1 = 1.

V(h,k) = V(0,1).

F(0,Y2),
VF = Y2 - k = 1/4a,
Y2 - 1 = 1/1 = 1,
Y2 = 2.

F(h,Y2) = F(0,2).

4. X^2 + 10X + Y^2 = 75.

Complete the square:
X^2 + 10X + (10/2)^2 + Y^2 = 75 + 25,
X^2 + 10X + 25 + Y^2 = 100,
The 1st 3 terms is a perfect square.
(X+5)^2 + Y^2 = 100,
(X+5)^2 + (Y-0)^2 = 100 = r^2,
Eq: (X-h)^2 + (Y-k)^2 = 100 = r^2.
C(h,k) = C(-5,0).

r^2 = 100.
r = 10.

5. X^2 + Y^2 - 4X + 12Y -6 = 0.

Complete the square:
X^2-4X+(-4/2)^2+Y^2+12Y+(12/2)^2-6=0,

X^2-4X+4 + Y^2+12Y+36-6=0+4+36,
(X-2)^2 + Y+6)^2 = 40+6=46

This is the Eq of a circle.

6. Eq1: x^2 + y^2 = 64,
Eq2: x^2 + 64y^2 = 64.

Multiply both sides of Eq1 by -1,and

-X^2 -Y^2 = -64
X^2 + 64Y^2 = 64.
Sum: 64y^2 = 0,
Y = 0.

Substitute "0" for Y in Eq1:
X^2 + 0^2 = 64,
X = +- 8.

Substitute +-8 for X in Eq2 and solve for Y in each case:
(8,0), (-8,0).

7. Substitute -2 for X and solve for Y.
Y = -29.

8. Y = X^3 + X^2 - 14X - 24.
The zeroes are the points where the graph crosses the X-axis(Y=0).

By trial and eror,a value of X(-2) was found that gives a Y value of 0 when
plugged into the given Eq.

(-2,0).
X = -2,
X+2 = 0.

Therefore, x+2 is a factor of the Eq.
So we divide the Eq by x+2 using long-
hand(synthetic) division and get:

X^2 - X - 12,
We now have Y = (X+2)(X^2 -X - 12).
Then we factor the Quadratic and get:

Y = (X+2)(X-4)(X+3).
X= -2,4,and -3.

9. Use same procedure as prob. 8 and
get: X = -3,-1, and 2.

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3. Solve the equation 6(3x + 1) = 8. Round the answer to four decimal places.

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