Explore BrainMass
Share

# Vertex, Asymptotes and Intercepts of Quadratic Equations

This content was STOLEN from BrainMass.com - View the original, and get the already-completed solution here!

D) The value of f(x) = 12 is
a) minimum
b) maximum

5) Find the x-intercepts and the y-intercepts

a) The x-coordinates of the intercepts are x=???
b) The y intercepts is ???

6) Find and label the vertex and line of the symmetry.

a) The vertex is ??? (type in an ordered pair)
b) The equation of the line of the symmetry is x = ???

7) Solve
a)
b) Find the x-intercepts of

8) Give exact and approximate solutions to three decimal places/

9) Solve the formula for the given letter. Assume that all variables represent non-negative numbers

10) Write a quadratic equation in the variable x having the given numbers as solutions. Type the equation in standard form
The solutions are -6 and 3

11) Solve by completing the square.

12) Give exact and approximate solutions to three decimal places.

a) Exact solutions are x=???
b) Approximate solutions to three decimal places are x=???

13) Determine the nature of the solutions of the equation.

a) One real solution
b) Two real solutions
c) Two non-real solutions

#### Solution Preview

Please see the attached file for the complete solution.

d) The value of f(x) = 12 is
a) minimum
b) maximum

5) Find the x-intercepts and the y-intercepts

a) The x-coordinates of the intercepts are x=???
b) The y intercepts is ???
f(x) = -(x^2 - 2x - 8) = -(x + 2)(x - 4)
(a) x-coordinates of the intercepts are x = {-2, 4}
(b) The y-intercept is (0, 8)

6) Find and label the vertex and line of the symmetry.

a) The vertex is ??? (type in an ordered pair)
b) The equation of ...

#### Solution Summary

Complete, Neat and Step-by-step Solutions are provided in the attached file.

\$2.19

## Graphs : Logartithms, Asymptotes and Interest Word Problems (10 Problems)

Please see the attached file for the fully formatted problems.

MTH133
Unit 4 - Individual Project

Name:

1) State the domain of the following:

a) g(x) = 5x/(x^2 + 25)

b) f(x) = sqrt(x + 6)

c) k(t) = 5t^2 - 6t + 2

d) k(x) = (3x - 3)/(x + 2)

e)

2) Suppose the graph of y=x^3 is shifted to obtain each the following graphs. What is the equation of the function, g(x), for each graph?

a)

b)

3) Consider the following graph of y = f(x).

a) If h(x) = f(x) + 3, what would the new coordinates of P be after the shift? Give answer in (x, y) form.

b) If , what would the new coordinates of P be after the reflection? Give answer in (x, y) form.

4) Consider the function f(x) = x^2 - 6x + 2 .

a) Find h, the x-coordinate of the vertex of this parabola.

b) Substitute the two integers immediately to the left of h and the two integers immediately to the right of h into the function to find the corresponding y. Fill in the following table. Make sure your x-values are in increasing order in your table.

x y

h =__

c) Use MS Excel or another web-based graphing utility to graph the function by plotting the points found in the table in part b. Paste your graph here.

5) Find the equations for the horizontal and vertical asymptotes of the following. Type none if the function does not have an asymptote.

a) f(x) = (2x + 1)/ (x - 4)
Horizontal:
Vertical:

b) g(x) = 3x/(x^2 + 4)
Horizontal:
Vertical:

c)
Horizontal:
Vertical:

d)
Horizontal:
Vertical:

6) Find the domain of the following:

a) g(x) = 5^x

b) g(x) = ln(x - 4)

c) g(t) = log(t + 2)

d) f(t) = 5.5e^t

7) Describe the transformations on the following graph of . State the placement of the horizontal asymptote and y-intercept after the transformation. For example, left 1 or rotated about the y-axis are descriptions.

a)
Description of transformation:
Equation(s) for the Horizontal asymptote(s):
y-intercept in (x, y) form:

b)
Description of transformation:
Equation(s) for the Horizontal asymptote(s):
y-intercept in (x, y) form:

8) Describe the transformations on the following graph of . State the placement of the vertical asymptote and x-intercept after the transformation. For example, left 1 or stretched vertically by a factor of 2 are descriptions.
a)
Description of transformation:
Equation(s) for the Vertical asymptote(s):
x-intercept in (x, y) form:

b)
Description of transformation:
Equation(s) for the Vertical asymptote(s):
x-intercept in (x, y) form:

9) The formula for calculating the amount of money returned for an initial deposit into a bank account or CD (certificate of deposit) is given by

A is the amount of the return.
P is the principal amount initially deposited.
r is the annual interest rate (expressed as a decimal).
n is the number of compound periods in one year.
t is the number of years.

Carry all calculations to six decimals on each intermediate step, then round the final answer to the nearest cent.

Suppose you deposit \$3,000 for 9 years at a rate of 6%.

a) Calculate the return (A) if the bank compounds annually (n = 1). Round your answer to the hundredth's place.
Show work in this space. Use ^ to indicate the power or use the Equation Editor in MS Word.

b) Calculate the return (A) if the bank compounds quarterly (n = 4). Round your answer to the hundredth's place.

c) Does compounding annually or quarterly yield more interest? Explain why.

Explain:

d) If a bank compounds continuously, then the formula used is
where e is a constant and equals approximately 2.7183.
Calculate A with continuous compounding. Round your answer to the hundredth's place.

e) A commonly asked question is, "How long will it take to double my money?" At 6% interest rate and continuous compounding, what is the answer? Round your answer to the hundredth's place.