Solving Equations Using Graphs Worksheet
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1Solving equations using graphs
Part of the graph of y = x
3
– 7x + 9 is shown on the grid.
(a) The graph of y = x
3
– 7x + 9 and the line with equation y = k, where k is an integer, have 3 points
of intersection. Find the greatest possible value of the integer k.
(b) By drawing a suitable straight line on the grid, find estimates of the solutions of the equation
x
3
– 6x – 2 = 0. Give your answers correct to 1 decimal place.
(c) State the number of solutions of each of the following equations:
(i) x
3
– 7x + 9 = 8
(ii) x
3
– 7x + 9 = 20 (iii) x
3
– 7x + 9 = 1
(d) The graph of y = x
3
– 7x + 9 and the line with equation y = k, where k is an integer, have 3 points
of intersection. Find the least possible value of the integer k.
(e) By drawing a suitable straight line on the grid, find estimates of the solutions of each of the
following equations. Give your answers correct to 1 decimal place.
(i) x
3
– 7x + 4 = 0
(ii) x
3
– 9x + 1 = 0
(iii) x
3
– 8x + 3 = 0
(f) Find the equation of the straight line you would need to draw on the graph above in order to
solve each of the following equations (don't actually draw the line):
(i) x
3
– 4x + 2 = 0
(ii) x
3
– 10x + 13 = 0 (iii) x
3
– 5x – 3 = 0
(iv) x
3
– 11x = 0
(v) 2x
3
– 12x + 8 = 0 (vi) 2x
3
4x + 7 = 0
+
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