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Grade 9 · Math · Algebra 1

9th grade Fit an exponential or quadratic model to data worksheet

6 printable versionsBuilding Confidence10 questions · answer keyFree · no account

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Fit an exponential or quadratic model to data

Grade 9 Math Worksheet - Building Confidence

NameDate

Circle the best answer, or write your answer on the line.

  1. Ren plotted duckweed spreading on the class pond, and the calculator fit y = 40(1.5)^x. What does the model predict for x = 3?

  2. Tala plotted fruit flies in the science-class jar, and the calculator fit y = 25(1.4)^x. What does the model predict for x = 2?

  3. Ari plotted a mug of cocoa cooling, and the calculator fit y = 50(0.8)^x. What does the model predict for x = 3?

  4. Bo plotted a water rocket's height, and the calculator fit y = -4.9x² + 28.4x + 1.2. What does the model predict for x = 3?

  5. Jun plotted bean plant growth against plant food, and the calculator fit y = -0.5x² + 6x + 3. What does the model predict for x = 4?

  6. Kira plotted visitors inside the science museum, and the calculator fit y = -3x² + 30x + 10. What does the model predict for x = 3?

  7. Read this first

    Use the table

    xy
    012
    120
    231
    350
    478
    5125

    Differences: 8, 11, 19, 28, 47. Second differences: 3, 8, 9, 19. Ratios (each y over the one before): 1.67, 1.55, 1.61, 1.56, 1.6.

  8. Luz recorded lily pads spreading on a park pond and worked out the differences and ratios. Which kind of model fits the data best?

    • Exponential: the ratios stay about the same.
    • Linear: the values keep going up.
    • Quadratic: the differences keep changing from row to row.

  9. Use the table

    xy
    015
    152
    279
    398
    4109
    5115

    Differences: 37, 27, 19, 11, 6. Second differences: -10, -8, -8, -5. Ratios (each y over the one before): 3.47, 1.52, 1.24, 1.11, 1.06.

  10. Milo recorded visitors inside the science museum and worked out the differences and ratios. Which kind of model fits the data best?

    • Quadratic: the second differences stay about the same.
    • Linear: the values keep changing.
    • Exponential: the differences keep changing from row to row.

  11. Use the table

    xy
    030
    144
    266
    399
    4151
    5226

    Differences: 14, 22, 33, 52, 75. Second differences: 8, 11, 19, 23. Ratios (each y over the one before): 1.47, 1.5, 1.5, 1.53, 1.5.

  12. Noah recorded algae growing in a fishbowl and worked out the differences and ratios. Which kind of model fits the data best?

    • Quadratic: the differences keep changing as the table goes down.
    • Exponential: the ratios stay about the same.
    • Linear: the values keep going up.

  13. Use the table

    xy
    25
    413
    625
    842
    1063
    1289

    Differences: 8, 12, 17, 21, 26. Second differences: 4, 5, 4, 5. Ratios (each y over the one before): 2.6, 1.92, 1.68, 1.5, 1.41.

  14. Pia recorded a bike's stopping distance against its speed and worked out the differences and ratios. Which kind of model fits the data best?

    • Quadratic: the second differences stay about the same.
    • Exponential: the differences keep changing down the table.
    • Linear: the values keep going up.
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9th grade Fit an exponential or quadratic model to data worksheet – printable
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About this worksheet

Fit an exponential or quadratic model to data. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

  • I can predict from a fitted exponential or quadratic model and find a residual.
  • I can tell from differences, second differences and ratios which kind of model fits, and pick the model whose predictions stay closest.
  • I can say when a model's prediction is reasonable and when it is far outside the data.

Standard: S-ID.B.6a

Words to know

exponential model y = a(b)^x: Start at a and multiply by b for each step of x.

quadratic model y = ax² + bx + c: A curve that bends; its second differences stay about the same.

ratio: One y-value divided by the one before.

second difference: The change between two differences.

highest point: Where a hill-shaped curve stops rising: x = −b ÷ (2a).

extrapolation: Predicting far outside the data's x-values.

Common mistakes

Your child multiplied by x instead of using it as a power. In an exponential model the factor is multiplied again for each step: 1.5^3 means 1.5 × 1.5 × 1.5.

Your child multiplied the start by the factor before doing the power. Only the factor is raised to the power; do the power first, then multiply by the start.

Your child squared the number in front of x² as well as x. Only x is squared: square x first, then multiply by the number in front.

Questions parents ask

What is the most common mistake with fit an exponential or quadratic model to data?

Your child multiplied by x instead of using it as a power. In an exponential model the factor is multiplied again for each step: 1.5^3 means 1.5 × 1.5 × 1.5.

Are these 9th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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