J17

(a) Draw suitable straight lines to find approximate solutions of the equations:
(i) 2 + 4x – 2x 2 = 0
(ii) 2x 2 – 3x – 2 = 0
(c) Find the range of values of x for which 2 + 3x – 2x 2 ≥ -5.
18.
18
Draw the graph of y = for 1 ≤ x ≤ 10, using scales of 1 cm to 1 unit on both
x
axes. Use the graph to solve approximately:
(a)
18 18 = x + 2 (b) + x = 10
x
x
(c) x 2 = 18
19. Draw the graph of y = x 2 – 2x + 2 for -2 ≤ x ≤ 4, using scales of 2 cm to 1 unit for x
and 1 cm to 1 unit for y.
By drawing other graphs, solve the equations:
(a) x 2 – 2x + 2 = 8
(b) x 2 – 2x + 2 = 5 – x
(c) x 2 – 2x – 5 = 0
20. Draw the graph of y = x 2 – 7x for 0 ≤ x ≤ 7, using scales of 2 cm to 1 unit on the x-
axis and 1 cm to 1 unit on the y-axis. Use your graph to solve the equations:
(a) x 2 – 7x + 9 = 0
(b) x 2 – 5x + 1 = 0
21. Complete the table below, for the function y = x 2 – x – 3; for -3 ≤ x ≤ 3
(a) Draw the curve y = x 2 – x – 3
(b) Write down the coordinates of the minimum point on your graph.
(c) For what range of values of x is y ≤ -1?
(d) Use your graph to solve the equation x 2 – x – 3 = 0.
x -3 -2 -1 0 1 2 3
x 2 4 1
-x 2 -1
-3 -3 -3
y= x 2 – x - 3 3 -3