Application of Quadratic Modeling
In previous lessons, we applied what we learned about linear modeling to word problems.
We are now going to do the same for quadratic functions.
This section will be a very brief introduction to solving quadratic word problems.
We will work with various types of word problems later in the course.
This concept is very important as you will be doing oodles and oodles of optimization problems in calculus.
Problem 1
Find the Quadratic equation that best models the data.
The following data represents the average maximum and minimum temperatures recorded each month in Raleigh, NC, over 6 months.
The temperatures recorded are in degrees Fahrenheit.
1. Identify the x and y axes. (Max/Min)
2. Using Desmos, plot the data.
3. Identify the domain and range intervals
4. Find the quadratic equation that best models the data.
5. What is the correlation coefficient?
6. Predict the minimum temperature if the maximum temperature is 90.
7. Predict the maximum temperature if the minimum temperature is 40.
Problem 2
This data represents the money in Sam's savings account over the years.
Let year 2000 = 0, then change all years accordingly.
1. Identify the x and y axes. (Yr/Amt)
2. Using your grapher, plot the data.
3. Identify the domain and range intervals.
4. Find the quadratic equation that best models the data.
5. What is the correlation coefficient?
6. How much money will Sam have in 2025?
7. When will Sam's account have approximately $1,645.50 in it?
Problem 3
A biologist took a count of the number of fish in a particular lake, and
recounted the lake's population of fish on each of the next six weeks.
1. Identify the x and y axes. (Week/Population)
2. Using Desmos, plot the data.
3. Identify the domain and range intervals.
4. Find a quadratic equation that best models the data.
5. What is the correlation coefficient?
6. Use the model to estimate the number of fish at the lake on week 10.
7. When will the number of fish increase to 1000?
Answers and work follow. Check your work and if you have questions - Ask!!