Quadratic Equations : Formulation of Real-Life Problems and Graphs
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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.
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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.
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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.
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Education
- BSc , Wuhan Univ. China
- MA, Shandong Univ.
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- "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."
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