4MA1/1HR Jan 2023, Question 15: Solving Equations by Graphical Methods

Part (a) · 2 marks

Fill in the missing y-values in the table for y = x³ − 3x + 2 at the given x-values.

1. 1Substitute each missing x into y = x³ − 3x + 2
2. 2x = −2: −8 + 6 + 2 = 0
3. 3x = −0.5: −0.125 + 1.5 + 2 = 3.375
4. 4x = 0: y = 2; x = 1.5: 3.375 − 4.5 + 2 = 0.875
5. 5x = 2: 8 − 6 + 2 = 4, so the values are 0, 3.375, 2, 0.875, 4

Answer0, 3.375, 2, 0.875, 4

Part (b) · 2 marks

Draw the curve y = x³ − 3x + 2 on the grid for x from −2 to 2.

1. 1Plot all points from the completed table: (−2, 0), (−1, 4), (−0.5, 3.375), (0, 2), (1, 0), (1.5, 0.875), (2, 4)
2. 2Draw a smooth curve through all the points

AnswerA smooth curve through (−2, 0), (−1, 4), (−0.5, 3.375), (0, 2), (1, 0), (1.5, 0.875), (2, 4)

Part (c) · 3 marks

Draw a suitable straight line on the grid and use the intersection to estimate the solution of 2x³ − 3x + 4 = 0 to one decimal place.

1. 1Divide by 2: x³ − 1.5x + 2 = 0
2. 2Rearrange to match the curve: x³ − 3x + 2 = −1.5x
3. 3Draw the line y = −1.5x, through (0, 0) and (−2, 3)
4. 4The line meets the curve at x ≈ −1.6

Answer−1.6

More past-paper questions on solving equations by graphical methods

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