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

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.

Â© BrainMass Inc. brainmass.com March 4, 2021, 6:16 pm ad1c9bdddfhttps://brainmass.com/math/graphs-and-functions/quadratic-equation-application-area-maximum-values-intercept-37799

#### Solution Preview

Please see the attached file for the complete solution.

Thanks for using BrainMass.

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 ...

#### Solution Summary

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