4MA1/1H Jan 2019, Question 6: Solving Equations by Graphical Methods

Part (a) · 1 mark

Fill in the missing y-values in the table for y = x² − 5x + 6 at x = 1 and x = 5.

1. 1x = 1: y = 1² − 5 × 1 + 6 = 2
2. 2x = 5: y = 5² − 5 × 5 + 6 = 6
3. 3Missing values: 2 and 6

Answer2 and 6

Part (b) · 2 marks

Draw the curve y = x² − 5x + 6 on the grid for x from 0 to 5.

1. 1Plot the points (0,6), (1,2), (2,0), (3,0), (4,2), (5,6)
2. 2Join the points with a smooth curve

AnswerA smooth curve through (0, 6), (1, 2), (2, 0), (3, 0), (4, 2), (5, 6)

Part (c) · 3 marks

Add a suitable straight line to the grid and use it to estimate the solutions of x² − 5x = x − 7.

1. 1x² − 5x = x − 7
2. 2So x² − 5x + 6 = x − 7 + 6 → x² − 5x + 6 = x − 1
3. 3Therefore, draw the line y = x − 1
4. 4Draw the straight line y = x − 1 on the grid
5. 5Find the points where the line y = x − 1 intersects the curve y = x² − 5x + 6
6. 6Read off the x-coordinates of the intersection points
7. 7The solutions are approximately 1.6 and 4.4

Answerx = 1.5 to 1.7 or x = 4.3 to 4.5

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