MAT 120 Ashford University Quadratic Equations Exercise Paper

For the discussion board assignment in each unit, you will complete the problem associated with the letter that you have been assigned by the instructor. Post the entire example/word problem you have been assigned from the textbook. Then fully explain how you would go about finding the solution. Please explain all steps in a way that a struggling classmate could understand and learn from your methods.

Professional communication is expected in all posts, which includes proper spelling and grammar, and providing source information when using outside resources.

Each unit Discussion Forum will be worth 5 points and will be graded on the following criteria:

• Problem is stated at the start of the post
• All work/explanation for assigned problem is shown
• Correct solution
• Proper grammar and spelling are used

This is the Letter assigned to me below and the entire question to that letter.

R. Section 8.1 The actual question is in the attachment please be sure to only do letter R.

MAT120 – College Algebra
Unit 5 DB Assignment
A. Section 5.5
Factor the difference of two squares. Assume that any variable exponents represent
whole numbers.
9𝑥 4 − 25𝑦 6
B. Section 5.7
Explain how to solve 𝑥 2 − 𝑥 = 6.
C. Section 8.1
Solve the equation by the square root property. If possible, simplify radicals or
rationalize denominators. Express imaginary solutions in the form 𝑎 + 𝑏𝑖.
(𝑥 + 3)2 = 64
D. Section 8.2
Solve the equation using the quadratic formula. Simplify solutions, if possible.
𝑥 2 + 3𝑥 − 20 = 0
E. Section 8.3
Describe how to find a parabola’s vertex if its equation is in the form
𝑓(𝑥) = 𝑎(𝑥 − ℎ)2 + 𝑘. Give an example.
F. Section 5.5
Factor the difference of two squares. Assume that any variable exponents represent
whole numbers.
9𝑥 2 − 25
G. Section 5.7
Use factoring to solve the polynomial equation. Check by substitution or by using a
graphing utility and identifying x-intercepts.
𝑥 3 + 4𝑥 2 − 25𝑥 − 100 = 0
H. Section 8.1
Determine the constant that should be added to the binomial so that it becomes a perfect
square trinomial. Then write and factor the trinomial.
𝑥 2 − 10𝑥
I. Section 8.2
What is the discriminant and what information does it provide about a quadratic
equation?
Compute the discriminant. Then determine the number and type of solutions for the given
equation.
𝑥 2 + 7𝑥 + 4 = 0
J. Section 8.3
Describe how to find a parabola’s vertex if its equation is in the form
𝑓(𝑥) = 𝑎𝑥 2 + 𝑏𝑥 + 𝑐. Use 𝑓(𝑥) = 𝑥 2 − 6𝑥 + 8 as an example.
K. Section 5.3
Factor the difference of two squares. Assume that any variable exponents represent
whole numbers.
64𝑥 2 − 25𝑦 2
L. Section 5.7
A piece of wire measuring 20 feet is attached to a telephone pole as a guy wire. The
distance along the ground from the bottom of the pole to the end of the wire is 4 feet
greater than the height where the wire is attached to the pole. How far up the pole does
the guy wire reach?
M. Section 8.1
Solve each quadratic equation by completing the square.
𝑥 2 + 6𝑥 = 7
N. Section 8.2
Solve each equation by the method of your choice. Simplify solutions, if possible.
𝑥 2 − 2𝑥 = 1
O. Section 8.3
The graph of a quadratic function is given.
Write the function’s equation, selecting from the following options:
𝑓(𝑥) = (𝑥 + 1)2 − 1
𝑔(𝑥) = (𝑥 + 1)2 + 1
ℎ(𝑥) = (𝑥 − 1)2 + 1
𝑗(𝑥) = (𝑥 − 1)2 − 1
P. Section 5.5
Factor the perfect square trinomials, or state that the polynomial is prime.
4𝑦 2 + 4𝑦 + 1
Q. Section 5.7
A pool measuring 10 meters by 20 meters is surrounded by a path of uniform width, as
shown in the figure. If the area of the pool and the path combined is 600 square meters,
what is the width of the path?
R. Section 8.1
Charter schools operate outside the constraints of regular public schools. They get public
money, but in most cases, their teachers are not unionized. This freedom has allowed a
minority of them to shine, building flexible, demanding programs that defy expectations.
But only 1 in 6 charter schools significantly outperforms traditional counterparts. And
more than a third underperform. The graph shows the number of U.S. students enrolled
in charter schools for selected years from 2000 through 2008.
The data shown can be modeled by the function 𝑓(𝑥) = 15𝑥 2 + 340, where 𝑓(𝑥)
represents the number of students enrolled in charter schools, in thousands, x years after
2000. Use this information to solve parts a and b of the following exercise.
a. According to the model, how many students, in thousands, were enrolled in
charter schools in 2008? Does this underestimate or overestimate the number
displayed by the graph? By how much?
b. According to the model, in which year will 3280 thousand students be enrolled in
charter schools?
S. Section 8.2
Write a quadratic equation in standard form with the given solution set.
{−2,6}
T. Section 8.3
The graph of a quadratic function is given.
Write the function’s equation, selecting from the following options:
𝑓(𝑥) = 𝑥 2 + 2𝑥 + 1
𝑔(𝑥) = 𝑥 2 − 2𝑥 + 1
ℎ(𝑥) = 𝑥 2 − 1
𝑗(𝑥) = −𝑥 2 − 1
U. Section 5.5
Factor using the formula for the sum or difference of two cubes.
𝑥 3 − 27
V. Section 5.7
A tree is supported by a wire anchored in the ground 5 feet from its base. The wire is 1
foot longer than the height that it reaches on the tree. Find the length of the wire.
W. Section 8.1
The function 𝑠(𝑡) = 16𝑡 2 models the distance, 𝑠(𝑡), in feet, that an object falls in t
seconds. Use this function and the square root property to solve the following exercise.
Express answers in simplified radical form. Then use your calculator to find a decimal
approximation to the nearest tenth of a second.
A skydiver jumps from an airplane and falls for 4800 feet before opening a
parachute. For how many seconds was the diver in a free fall?
X. Section 8.2
The hypotenuse of a right triangle is 6 feet long. One leg is 2 feet shorter than the other.
Find the lengths of the legs. Round to the nearest tenth of a foot.
Y. Section 8.3
Find the coordinates of the vertex for the parabola defined by the given quadratic
function.
𝑓(𝑥) = 3𝑥 2 − 12𝑥 + 1
Z. Section 5.5
Factor using the formula for the sum or difference of two cubes.
27𝑦 3 + 1