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Quadratic Equation Application Word Problems : Area, Maximum Values and Intercepts

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1. Given the quadratic equation y=-x2 + 8x + 9
a. Find the x and y coordinates of the vertex

b. What is the y-intercept?

c. What are the x-intercepts?

d. If you graph the parabola, would it open up or down?

2. You have enough grass seed to cover an area of 300 square feet. You want to install fencing around the area you are going to seed and you decide that the width of the area should be 10 feet less than the length. Using a quadratic equation, find the length and width of the area.

3. Ann receives all emails that customers send her company regarding technical issues. On an average 8 hour day, the number of emails she receives every day can be modeled with the equation C = -x2+6x+16, where x is the number of hours she has been at work, and C Is the number of emails Ann receives. During what hour of her day does she receive the most (maximum) emails?

a. Calculate the y-intercept and explain how this value relates to the emails Ann receive.

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Solution Summary

Quadraitic equation problems involving area and maximum values are solved. The practical meanng of intercepts is discussed.

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Please help me understand the three problems listed below by showing how the solution was determined. Willing to release all 13 credits for showing all work and solutions. Thank you.

1. Given the quadratic equation y=-x2 + 8x + 9
a. Find the x and y coordinates of the vertex

So, the vertex is (4, 25), namely, the x and y coordinates of the vertex are 4 and 25, respectively.

b. What is the y-intercept?
In order to find the y-intercept, we need to let x=0, so

So, the ...

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  • 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."
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  • "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!"
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