Purchase Solution

# Quadratic Equations : Formulation of Real-Life Problems and Graphs

Not what you're looking for?

Please see the attached file for the fully formatted problems.

1. Can a graph be used to solve any quadratic equation? Why or why not?

2. Look at the graph below and comment on the sign of D or the discriminant. From the quadratic equation based on the information provided and find its solution.

3. Formulate two word problems from day-to-day life that can be translated to quadratic equations.

4. Based on your readings, list and describe the different methods for solving quadratic equations. Provide examples for each of the methods you listed.

##### Solution Summary

Graphs of quadratic equations are investigated and two real-life situations are formulated as quadratic equations. The solution is detailed and well explained.

##### Solution Preview

Please see the attached file for the full solution.
Thanks for using BrainMass.

1. Can a graph be used to solve any quadratic equation? Why or why not?
Yes. Plotting a graph of any quadratic function, if there are no intersections with x-axis, we can conclude that the corresponding quadratic equation has no solution. If there are two intersection points, then we can conclude that the corresponding quadratic equation has two solutions. If there is only one intersection point, then we can conclude that the corresponding quadratic equation has two equal solutions.
2. Look at the graph below and comment on the sign of D or the discriminant. From the quadratic equation based on the information provided and find it solution.

Since there are tow intersection points, we know that this quadratic equation has two real roots. Hence, the sign of D or the discriminant is greater than zero.
Based on the information provided, we know two solutions are x=-1 and x=0.67.
3. Formulate two word problems from day-to-day life that can be translated to quadratic equations.
...

Solution provided by:
###### Education
• BSc , Wuhan Univ. China
• MA, Shandong Univ.
###### Recent Feedback
• "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
• "excellent work"
• "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
• "Thank you"
• "Thank you very much for your valuable time and assistance!"

##### Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

##### Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

##### Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

##### Probability Quiz

Some questions on probability

##### Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.