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Algebra 1

8.12.5 Practice

Algebra 18.12.5 Practice

8.12.5 Practice

8.12.5 • Practice

Access the Desmos guide PDF for tips on solving problems with the Desmos graphing calculator.

Complete the following questions to practice the skills you have learned in this lesson.

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  1. Enter the given data into Desmos, then calculate the regression approximation to determine the curve of best fit.
    x 1 y 1
    2 56
    5 116
    8 155
    11 205
    17 230

What is the equation for the curve of best fit that models the data?

  1. y = − 0.93 𝑥 2 + 22.63 x + 10.48
  2. y = − 0.69 x 2 + 24.83 x + 8.07
  3. y = − 3.11 x 2 + 16.32 x + 8.94
  4. y = − 0.7 x 2 + 35.93 x + 8.19
  1. Enter the given data into Desmos, then calculate the regression approximation to determine the curve of best fit.
    x 1 y 1
    3 105
    9 250
    14 349
    23 400
    37 258

What is the equation for the curve of best fit that models the data?

  1. y = − 0.74 x 2 + 34.32 x + 7.44
  2. y = − 0.62 x 2 + 17.45 x + 9.64
  3. y = − 2.31 x 2 + 24.711 x + 3.25
  4. y = − 0.56 x 2 + 38.74 x + 5.31
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  1. Enter the given data into Desmos, then calculate the regression approximation to determine the curve of best fit.
    x 1 y 1
    0.2 6.5
    0.35 6.74
    0.66 6.31
    1 4.95
    1.5 1.2

What is the equation for the curve of best fit that models the data?

  1. y = − 5.1 x 2 + 9.2 x + 7.14
  2. y = − 4.31 x 2 + 3.2 x + 6.08
  3. y = − 3.1 x 2 + 2.6 x + 7.93
  4. y = − 6.3 x 2 + 8 x + 10.6
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  1. Enter the given data into Desmos, then calculate the regression approximation to determine the curve of best fit.
    x 1 y 1
    0.3 25
    0.6 36
    1.2 45
    1.8 33
    2.3 12

What is the equation for the curve of best fit that models the data?

  1. y = − 35.78 x 2 + 45.21 x + 3.74
  2. y = − 3.72 x 2 + 7.34 x + 8.67
  3. y = − 30.84 x 2 + 49.61 x + 8.99
  4. y = − 25.41 x 2 + 59.28 x + 9.64
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For questions 5 – 9, use the following information.

The path of a toy rocket after launch is modeled by the following data set. The height of the rocket, in feet, y , corresponds to the number of seconds passed, x .
x 1 y 1
0.4 20
1 41
1.5 52
2.3 60
3.5 52

  1. What is the equation for the curve of best fit that models the flight of the toy rocket?
  1. y = − 9.2 x 2 + 46 x + 3.51
  2. y = − 4.2 x 2 + 34 x + 6.34
  3. y = − 11.9 x 2 + 30.2 x + 3.64
  4. y = − 6.1 x 2 + 31 x + 1.24
  1. Approximately how high will the rocket be 2 seconds after launch?
  1. 61.00 feet
  2. 58.71 feet
  3. 53.60 feet
  4. 45.91 feet
  1. At what approximate times after launch will the rocket have a height of 20 feet?
  1. 0.82 seconds after launch and 4.18 seconds after launch
  2. 0.52 seconds after launch and 4.48 seconds after launch
  3. 0.39 seconds after launch and 4.61 seconds after launch
  4. 0.26 seconds after launch and 4.74 seconds after launch
  1. Approximately how long will it take the rocket to reach its maximum height?
  1. 5.08 seconds
  2. 3.20 seconds
  3. 2.50 seconds
  4. 1.73 seconds
  1. Approximately how long will it take for the rocket to land on the ground?
  1. 6.12 seconds
  2. 5.08 seconds
  3. 4.63 seconds
  4. 2.50 seconds

For question 10, Maria has found a curve of best fit using the equation below.

y = − 0.46 x 2 + 14 x + 17


  1. Maria is asked to predict the y -value on her curve when x = 10 . To do this, she graphs the function x = 10 and analyzes the intersection point of the curve and the line.

    What is the y -value Maria is asked to predict?
  1. 111
  2. 105
  3. 93
  4. 10
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