Worksheets · Algebra 1

Using statistical models worksheet

A model is an equation fitted to real data. Put an x in to predict a y. To find which x gives a certain y, set the model equal to that y and solve: a quadratic model can give two answers, and both may make sense. The starting value of an exponential model, its y-intercept, is the amount at the start of the time count.

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Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Using Statistical Models

Date Period

Answer each question.

  1. A model for the temperature in a greenhouse, in degrees Fahrenheit, is y=−0.2x2+5.6x+60.8, where x is the number of hours after midnight. For which values of x is y=97? Round to the nearest whole number.
  2. If y is the number of wolves in a park x years after 1980, a model is y=47(1.12)x. What does the y-intercept mean?
  3. Find the line of best fit and r2, each to the nearest hundredth.x345678y013−3−6−9
  4. A model for a car's gas mileage, in miles per gallon, is y=−0.02x2+2.28x−32.98, where x is its speed in miles per hour. Find y when x=63, to the nearest tenth.
  5. If y is the value of a house, in thousands of dollars, x years after 2000, a model is y=75(0.9)x. What does the y-intercept mean?
  6. Find the line of best fit and r2, each to the nearest hundredth.x369121518y21118253946
  7. A model for the cost to make each item, in dollars, is y=0.02x2−0.44x+11.42, where x is the number made, in hundreds. For which values of x is y=10? Round to the nearest whole number.
  8. If y is the number of wolves in a park x years after 2000, a model is y=45(0.95)x. What does the y-intercept mean?
  9. Find the line of best fit and r2, each to the nearest hundredth.x5811141720y5978106121147164
  10. A model for the height of a model rocket, in feet, is y=−16x2+128x+437, where x is the number of seconds after launch. For which values of x is y=558? Round to the nearest whole number.
  11. If y is the number of oysters in a bay, in thousands, x years after 1980, a model is y=44.2(0.9)x. What does the y-intercept mean?
  12. Find the line of best fit and r2, each to the nearest hundredth.x24681012y343744536769
  13. A model for the cost to make each item, in dollars, is y=0.03x2−1.62x+27.87, where x is the number made, in hundreds. Find y when x=16, to the nearest tenth.
  14. If y is the number of oysters in a bay, in thousands, x years after 2000, a model is y=36.9(1.04)x. What does the y-intercept mean?
  15. Find the line of best fit and r2, each to the nearest hundredth.x1357911y71217152126
  16. A model for the height of a model rocket, in feet, is y=−16x2+224x+30, where x is the number of seconds after launch. Find y when x=4, to the nearest tenth.
  17. If y is the number of farms in a county, in hundreds, x years after 1950, a model is y=78(1.06)x. What does the y-intercept mean?
  18. Find the line of best fit and r2, each to the nearest hundredth.x123456y2022181291
  19. A model for a store's weekly profit, in hundreds of dollars, is y=−0.12x2+4.8x+13, where x is the price of an item, in dollars. For which values of x is y=43? Round to the nearest whole number.
  20. If y is the population of a town, in thousands, x years after 2000, a model is y=18.3(0.85)x. What does the y-intercept mean?

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Using Statistical ModelsAnswer keyVersion 1

Date Period

Answer each question.

  1. A model for the temperature in a greenhouse, in degrees Fahrenheit, is y=−0.2x2+5.6x+60.8, where x is the number of hours after midnight. For which values of x is y=97? Round to the nearest whole number.x≈10 and x≈18
  2. If y is the number of wolves in a park x years after 1980, a model is y=47(1.12)x. What does the y-intercept mean?In 1980 there were about 47 wolves in the park.
  3. Find the line of best fit and r2, each to the nearest hundredth.x345678y013−3−6−9y=−2.06x+8.98, r2=0.72
  4. A model for a car's gas mileage, in miles per gallon, is y=−0.02x2+2.28x−32.98, where x is its speed in miles per hour. Find y when x=63, to the nearest tenth.31.3
  5. If y is the value of a house, in thousands of dollars, x years after 2000, a model is y=75(0.9)x. What does the y-intercept mean?In 2000 the house was worth about 75 thousand dollars.
  6. Find the line of best fit and r2, each to the nearest hundredth.x369121518y21118253946y=2.96x−7.60, r2=0.99
  7. A model for the cost to make each item, in dollars, is y=0.02x2−0.44x+11.42, where x is the number made, in hundreds. For which values of x is y=10? Round to the nearest whole number.x≈4 and x≈18
  8. If y is the number of wolves in a park x years after 2000, a model is y=45(0.95)x. What does the y-intercept mean?In 2000 there were about 45 wolves in the park.
  9. Find the line of best fit and r2, each to the nearest hundredth.x5811141720y5978106121147164y=7.11x+23.57, r2=1.00
  10. A model for the height of a model rocket, in feet, is y=−16x2+128x+437, where x is the number of seconds after launch. For which values of x is y=558? Round to the nearest whole number.x≈1 and x≈7
  11. If y is the number of oysters in a bay, in thousands, x years after 1980, a model is y=44.2(0.9)x. What does the y-intercept mean?In 1980 there were about 44.2 thousand oysters in the bay.
  12. Find the line of best fit and r2, each to the nearest hundredth.x24681012y343744536769y=3.91x+23.27, r2=0.96
  13. A model for the cost to make each item, in dollars, is y=0.03x2−1.62x+27.87, where x is the number made, in hundreds. Find y when x=16, to the nearest tenth.9.6
  14. If y is the number of oysters in a bay, in thousands, x years after 2000, a model is y=36.9(1.04)x. What does the y-intercept mean?In 2000 there were about 36.9 thousand oysters in the bay.
  15. Find the line of best fit and r2, each to the nearest hundredth.x1357911y71217152126y=1.71x+6.05, r2=0.92
  16. A model for the height of a model rocket, in feet, is y=−16x2+224x+30, where x is the number of seconds after launch. Find y when x=4, to the nearest tenth.670.0
  17. If y is the number of farms in a county, in hundreds, x years after 1950, a model is y=78(1.06)x. What does the y-intercept mean?In 1950 the county had about 78 hundred farms.
  18. Find the line of best fit and r2, each to the nearest hundredth.x123456y2022181291y=−4.00x+27.67, r2=0.89
  19. A model for a store's weekly profit, in hundreds of dollars, is y=−0.12x2+4.8x+13, where x is the price of an item, in dollars. For which values of x is y=43? Round to the nearest whole number.x≈8 and x≈32
  20. If y is the population of a town, in thousands, x years after 2000, a model is y=18.3(0.85)x. What does the y-intercept mean?In 2000 the town had about 18.3 thousand people.

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

How to do these

A model is y=0.25x2−10x+200. For which x is y=136?

  1. Set the model equal to 136: 0.25x^2 - 10x + 64 = 0.
  2. Use the quadratic formula: x = (10 ± sqrt(100 - 64)) / 0.5.
  3. That is (10 ± 6) / 0.5, so x = 8 or x = 32.

The answer is x=8 and x=32.

Where students go wrong

Keeping only one answer. When a quadratic model is set equal to a value it usually crosses it twice, once going down and once coming back up, and both x-values answer the question unless the context rules one out.

Also called quadratic regression, exponential regression, interpreting models, using a model to predict or line of best fit and r squared.

What you can put on this worksheet

Quadratic models: evaluate, and solve for x
A model for a car's gas mileage, in miles per gallon, is y=−0.02x2+2.24x−33.72, where x is its speed in miles per hour. Find y when x=59, to the nearest tenth. → 28.8
What the y-intercept means
If y is the value of a house, in thousands of dollars, x years after 1900, a model is y=58.4(1.04)x. What does the y-intercept mean? → In 1900 the house was worth about 58.4 thousand dollars.
The line and r squared
Find the line of best fit and r2, each to the nearest hundredth.
x35791113y152422292935
→ y=1.74x+11.72, r2=0.89

Questions about these worksheets

Yes. Every using statistical models sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Algebra 1 is usually taken around 8th or 9th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the using statistical models questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

You pick from 3: quadratic models: evaluate, and solve for x, what the y-intercept means and the line and r squared. Tick as many as you want and set how many of each, or let it spread them evenly.

Keeping only one answer. When a quadratic model is set equal to a value it usually crosses it twice, once going down and once coming back up, and both x-values answer the question unless the context rules one out.