The solutions of the quadratic equation Ax^2+Bx+C=0 are called roots and are given by a famous equation called the Quadratic Formula . In the quadratic formula, the terms B^2-4AC underneath the radical have a special name: the Discriminant .

Discuss the relationship between the discriminant of a quadratic polynomial and the quantity of real roots it possesses. Explain the positioning of the roots of the polynomial on its graph with respect to the discriminant and the sign of the discriminant.

# Category: Algebra

The solutions of the quadratic equation Ax^2+Bx+C=0 are called roots and are given by a famous equation called the Quadratic Formula . In the quadratic formula, the terms B^2-4AC underneath the radical have a special name: the Discriminant .

Discuss the relationship between the discriminant of a quadratic polynomial and the quantity of real roots it possesses. Explain the positioning of the roots of the polynomial on its graph with respect to the discriminant and the sign of the discriminant.

## Do not write with red ink/red pencil.

UNIT 2 TEST Take-home

NAME

MAT1033

Show all your work and attach notebook paper if needed but write your answers in the blanks/graph

grids provided on this test sheet. Do Not write with red ink/red pencil.

## Payments one makes?

How does one decide if a house is affordable? How does the listed price of a house translate to the actual monthly mortgage

payments one makes?

Watch the video introduction on the SIR Model.

2. Set up the beginning section of your spreadsheet. (This will be submitted by the end of the week for a grade.)

3. Discussion participation where you will share your understanding and also ask others for assistance if needed. You are also required to respond to at least one other student in the forum. (Proper and thoughtful participation in the discussion is also a portion of the Unit 1 grade.

Please share your previous experiences with math, including previous math courses. How do you view the area of contemporary math? How do you see using it after taking this course?

Please also share whatever else you think would be helpful for me to know.

Address all of the prompts and questions, showing your work and explaining your solutions or answers to all of the questions.

Make sure to post the equation for a classmate to graph. Make sure you have the answer so that you can check any classmate’s work who responds to your initial post.

Linear Extrapolation

Last week you were introduced to graphing linear functions. One common use of linear equations is linear extrapolation, where you take real data to make a linear equation, and then use it to make predictions.

For this math-based discussion, follow the steps below. Type all math in the discussion using the Blackboard Math Editor. Make sure you are giving details and explaining each step in your post.

Research the sales or revenue for a company and write 2 ordered pairs in the form (year, dollars).

Find the slope between those two points and interpret what it means in context for the company you chose.

Use Point-Slope Form to write the equation of the line between these points.

Use your equation to predict future sales or revenue, and discuss whether you think your prediction will be accurate and why/why not

Your donut shop has perfected a method for the perfect glazed icing by slowly mixing whole milk to confectioner’s sugar while exposed to low heat. Your mixing tank starts with 10 fluid ounces of milk and 10 ounces of sugar. You continue adding sugar at a rate of 10 ounces per minute and milk at 1 ounce per minute, as depicted by the two equations below:

S equals 10 plus 10 t

M equals 10 plus 1 t

Where S represents the number of ounces of sugar, M represents the ounces of milk, and t represents the time in minutes. The ideal icing will have a ratio of 8 ounces of sugar per ounce of milk.

Assessment Instructions

Show and explain all steps in your responses to the following parts of the assignment. All mathematical steps must be formatted using the equation editor.

Part 1: Create a rational equation to represent the concentration (C) in ounces of sugar per ounce of milk.

Part 2: Find the domain of the concentration equation.

Part 3: Will we ever encounter a time where the rational equation is undefined? Explain your reasoning.

Part 4: Calculate the concentration after five minutes.

Part 5: How long does it take to reach a concentration of 8 ounces of sugar per ounce of milk?

In the 1939 movie The Wizard of Oz, upon being presented with a Th.D. (Doctor of Thinkology), the Scarecrow proudly exclaims, “The sum of the square roots of any two sides of an isosceles triangle is equal to the square root of the remaining side.” Analyze the statement made by the Scarecrow. Present your analysis and give a complete description of the triangles that satisfy the statement.

Find another example of math being used in:

Movies, television, popular culture, art, music and harmonics, scientific research papers, newspapers or magazine articles, nature and natural phenomena, voting, national security, manufacturing, logistics, transportation, healthcare, business, economics, or some noteworthy or pivotal historical moment.

Research and explain whether or not the math was used correctly.