Grade 9 · Math · Algebra 1

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

6 printable versionsChallenge Me10 questions · answer keyFree · no account

Level: Building Confidence · On Level · Challenge Me

When it’s done, scan the sheet with your phone and PencilGo marks it and picks the next one. Create a free account

Version

Fit an exponential or quadratic model to data

Grade 9 Math Worksheet - Challenge Me

NameDate

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

Ren plotted a play ball tossed straight up, and the calculator fit y = -5x² + 16x + 1.5. At what x does the model reach its highest value?
Tala plotted a water rocket's height, and the calculator fit y = -5x² + 26x + 1. At what x does the model reach its highest value?
Zee plotted visitors inside the science museum, and the calculator fit y = -2.5x² + 23x + 8. At what x does the model reach its highest value?
Ari plotted bean plant growth against plant food, and the calculator fit y = -0.6x² + 7.8x + 4. At what x does the model reach its highest value?
The calculator's fit, rounded: y = 30(1.4)^x. Bo recorded duckweed spreading on the class pond, and the calculator fit y = 30(1.4)^x. In which whole week does the model first go above 200?
The calculator's fit, rounded: y = 15(1.7)^x. Esme recorded fruit flies in the science-class jar, and the calculator fit y = 15(1.7)^x. In which whole day does the model first go above 400?
The calculator's fit, rounded: y = 300(0.8)^x. Kira recorded a wet beach towel drying in the sun, and the calculator fit y = 300(0.8)^x. In which whole hour does the model first go below 30?
8.
Milo plotted a water rocket's height, and the calculator fit y = -4.9x² + 29.4x + 1.5. Should Milo trust the model's prediction for x = 12?
- No: a model can never be used to predict.
- Yes: the model predicts about -351, so that is what will happen at that moment.
- No: x = 12 is far outside the data, 0 to 5, so the model may not hold there.
9.
Noah plotted visitors inside the science museum, and the calculator fit y = -3x² + 28x + 9. Should Noah trust the model's prediction for x = 4.5?
- Yes: x = 4.5 is inside the data, where the model fits the dots well.
- No: a model can never be used to predict.
- No: there is no dot at x = 4.5, so the model cannot be trusted there.
10.
Pia plotted a bowl of soup cooling, and the calculator fit y = 60(0.93)^x. Should Pia trust the model's prediction for x = 10?
- Yes: x = 10 is inside the data, where the model fits the dots well.
- No: a model can never be used to predict.
- No: there is no dot at x = 10.

9th grade Fit an exponential or quadratic model to data worksheet – printable — Print: 1 2 3 4 5 6

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.

More algebra 1

See all Algebra 1

Every sheet you scan goes into your child’s record: dated, marked and ready for the year-end portfolio. Homeschool records