Algebra Answers

7: The average income, I, in dollars, of a lawyer with an age of x years is modeled with the following function: I = -425x^2 + 45,500x – 650,000
What is the youngest age for which the average income of a lawyer is $450,000?

Round answer to nearest year. Answer: _____

8: The average annual income, I, in dollars of a lawyer with an age of x years is modeled with the following function:

I = 425x^2 + 45,500x – 650,000

According to this model, what is the maximum average annual income in dollars, a lawyer can earn?

Round to the nearest whole dollar.

Answer: ______

1: A rectangle's width is 6 feet less than its length. Writer a quadratic function that expresses the rectangle's area in terms of its length.

A: A(L) = L^2 - 6L

B: A(L) L^2 +6L

C: A(L) = LW

D: A(L) = L -6

2: A rectangle's width is 5 feet less than its length. If the area of the rectangle is 546 square feet, what is its length, in feet?

_______________

3: A tennis ball machine serves a ball vertically into the air from the height of 2 feet, with an initial speed of 110 feet per second. Which equation correctly models the ball's height as a function of time?

A: h(t) = - 16t^2 -2t +110

B: h(t) = - 16t^2 + 110t + 2

C: h(t) = - 16t^2 – 110t +2

D: h(t) = -16t^2 +2t + 110

1: Solve the equation:

(x + 3)(x – 2) = 0

Enter the solution with the lowest value. ______

2: Solve the equation:

(3x + 2)(x – 5) = 0

Enter the solution with the highest value. ______

4: Solve by factoring:
x^2 – 13x – 14 = 0

A: x = - 14, x = 1
B: x = -1, x = 14
C: x = -2, x = 7

5: Simplify: √-36

The root extends over the -36, just as all of the other numbers starting with √ : √-36

A: -6i

B: 6i √2

C: 6i

D: -6i √2

6: Simplify: -√-75

A: -5i

B: 5i

C: -5i√2

D: -5i√3

9: In the function y + 2 = 1/3(x – 4)^2 , what effect does the number 4 have on the graph, as compared to the graph of y = x^2

A: It shifts the graph 4 units to the right.
B: It shifts the graph 4 units to the left.
C: It shifts the graph up 4 units.
D: It shifts the graph down 4 units.

10: A vertical shift is an example of a non-rigid transformation.
A: True
B: False

7: Consider the function y = x^2 + 5x – 2 , what would happen to the graph if (x – 3) was submitted in place of the x

A: The graph would shift 3 units to the left
B: The graph would shift 3 units to the right
C: The graph would shift up 3 units.
D: The graph would shift down 3 units.

8: Which of the following accurately depicts the transformation of y = x^2 to the function shown below.
Y = 2(x – 3)^2 + 5

A: Shift left 3 units, shrink vertically to ½ of the original height, then shift up 5 units.
B: Shift up 3 units, stretch horizontally by a factor of 2 , then shift left 5 units.
C: Shift 5 units right, stretch vertically by a factor of 3 , then shift up 2 units.
D: Shift right 3 units, stretch vertically by a factor of 2, then shift up 5 units.

3: In the function y + 3 = (2x)^2 + 1, what effect does the number 2 have on the graph, as compared to the graph of y = x^2

A: It stretches the graph horizontally by a factor of 2
B: It shrinks the graph vertically to ½ the original height.
C: It stretches the graph vertically by a factor of 2
D: It shrinks the graph horizontally to ½ the original width.

4: Which of the following describes the non-rigid transformation in the function shown below?
Y + 5 = -2(x – 1 )^2

A: A graph is shifted 1 unit right
B: A graph is shifted 5 units down
C: A graph is reflected across the x-axis
D: A graph is stretched vertically by a factor of 2.

1: In the function y+ 3(x + 1 )^2 + 7 , what effect does the number 7 have on the graph, as compared to the graph of the function y = x^2?

A: It shifts the graph 7 units to the right.
B: It shifts the graph up 7 units.
C: It shifts the graph 7 units to the left.
D: It shifts the graph down 7 units.

2: In the function y = -3x^2 + 1 , what effect does the negative sign have on the graph, as compared to the graph of y = x^2

A: It shrinks the graph horizontally by a factor of 3.
B: It stretches the graph horizontally by a factor of 3.
C: It shrinks the graph vertically by a factor of 3
D: It reflects the graph across the x-axis.

: you have a coupon for your favorite clothing store for $ 25 off any purchase of more than $50. The store is also running a 20%- off sale on its entire inventory. Let x be the original price, f(x) be the price with the 4 25 coupon applied, and g(x) be the price with the 20% discount applied.

a. Write an expression for f(x)

b. Write an expression for g(x)

c.What would the expression (f o g)(x) represent?

d. What would the expression (g o f)(x) represent?

e. If the store allows you to apply both the 20% discount and the $25- off coupon, does it matter which you apply first? How do you know ?

: Given the table below, evaluate the following:
X -3 -2 -1 0 1 2 3 4 5
f(x) 10 20 30 40 50 60 70 80 90
g(x) -1 -2 -3 -4 -5 -6 -7 -8 -9

a. (3f + 2g)(1)

b. (f o g)(-1)

Express the following function, F(x) as a composition of two functions f and g.

x^2
F(x) = -----------
(x^2 + 4)

: Solve the following system of equations algebraically. Verify the solution either graphically or by using matrices.
3x – y = 0
5x + 2y = 22


: Solve the following system of equations algebraically. Verify the solution either graphically or by using matrices.
8x -2y = 5
-12x +3y = 7