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Grade 9 · Math · Algebra 1

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

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Fit an exponential or quadratic model to data

Grade 9 Math Worksheet

NameDate

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

  1. Ren plotted algae growing in a fishbowl, and the calculator fit y = 30(1.35)^x. What does the model predict for x = 4, to the nearest whole number?

  2. Tala plotted lily pads spreading on a park pond, and the calculator fit y = 8(1.45)^x. What does the model predict for x = 5, to the nearest whole number?

  3. Zee plotted a bowl of soup cooling, and the calculator fit y = 62(0.94)^x. What does the model predict for x = 6, to the nearest whole number?

  4. Bo plotted duckweed spreading on the class pond, and the calculator fit y = 35(1.45)^x. What is the residual for the dot at x = 4, to the nearest tenth?

  5. Esme plotted a water rocket's height, and the calculator fit y = -4.9x² + 27.5x + 1.5. What is the residual for the dot at x = 3, to the nearest tenth?

  6. Jun plotted how high a play ball bounces back, and the calculator fit y = 120(0.68)^x. What is the residual for the dot at x = 2, to the nearest tenth?

  7. Kira plotted visitors inside the science museum, and the calculator fit y = -2.5x² + 26x + 12. What is the residual for the dot at x = 5, to the nearest tenth?

  8. Read this first

    Table, x | data | line | quadratic

    0 | 2.9 | 13 | 3; 2 | 12.8 | 13 | 13; 4 | 19.9 | 14 | 20; 6 | 22.7 | 14 | 23; 8 | 22 | 15 | 22; 10 | 15.8 | 16 | 17; 12 | 6.5 | 16 | 7. The line is y = 0.3x + 12.6; the quadratic model is y = -0.5x² + 6.4x + 2.5. Predictions are rounded to whole numbers.

  9. Milo fit a line and a quadratic model to bean plant growth against plant food. The table lists both models' predictions. Which model fits the data better?

    • The quadratic model: its predictions stay close to every dot.
    • The line, because it is closer at x = 10.
    • Both fit equally well.
    • The line, because a line is simpler and easier to read than a curve.

  10. Table, x | data | line | exponential

    0 | 6 | -15 | 6; 1 | 10 | 6 | 10; 2 | 18 | 28 | 17; 3 | 29 | 49 | 29; 4 | 47 | 71 | 50; 5 | 95 | 92 | 85; 6 | 139 | 113 | 145. The line is y = 21.4x - 14.9; the exponential model is y = 6(1.7)^x. Predictions are rounded to whole numbers.

  11. Noah fit a line and an exponential model to lily pads spreading on a park pond. The table lists both models' predictions. Which model fits the data better?

    • The line, because it is closer at x = 5.
    • The line, because a line is simpler and easier to work with than a curve.
    • Both fit equally well.
    • The exponential model: its predictions stay close to every dot.

  12. Table, x | data | line | quadratic

    0 | 11 | 39 | 10; 1 | 32 | 41 | 32; 2 | 45 | 44 | 48; 3 | 63 | 46 | 60; 4 | 67 | 49 | 68; 5 | 68 | 51 | 70; 6 | 69 | 53 | 68; 7 | 63 | 56 | 60; 8 | 47 | 58 | 48; 9 | 31 | 61 | 32. The line is y = 2.4x + 38.9; the quadratic model is y = -2.4x² + 24x + 10. Predictions are rounded to whole numbers.

  13. Pia fit a line and a quadratic model to visitors inside the science museum. The table lists both models' predictions. Which model fits the data better?

    • The line, because it is closer at x = 2.
    • The quadratic model: its predictions stay close to every dot.
    • Both fit equally well.
    • The line, because a line is simpler.
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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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