J17

Draw on the same axes the graph of y = 8x – 7.
By considering the points of intersection of the two graphs, a certain quadratic
equation in x can be solved. Write down and simplify the equation and obtain its
roots from the graphs.
12. Some of the values of the function 3 – 3x – x 2 for domain -5 ≤ x ≤ 2 are given in the
following table. Complete the table and use it to draw the graph of the function.
x -5 -4 -3 -2.5 -2 -1.5 -1 0 1 2
3 – 3x – x 2 -7 …. 3 4.25 5 … 5 3 -1 …
From your graph find:
(a) The greatest value of the function and the corresponding value of x,
(b) The range of values of x for which the function has values greater than 2.
13. Copy and complete the following table for value of: x(5 – x).
x 0 0.5 1 2 2.5 3 4 4.5 5
x (5-x) 2.25 4 4 2.25 0
Draw the graph of y = x(5 – x) from x = 0 to x = 5,using a scale of 2 cm to 1 unit on
each axis.
6
With the same axes, draw the graph of y = from x = 0 to x = 5.
x +1
Use your graphs to obtain:
(a) an equation whose solutions are the points of intersection of the two graphs.;
6
(b) the range of values of x for which x(5 – x) > .
x +1
14. Assuming the graph of y = x 2 + x + 1 has been drawn; find the equation of the line
which should be drawn to solve the equations:
(a) x 2 + x +1 = 6 (b) x 2 + x + 1 = 0
(c) x 2 + x – 3 = 0 (d) x 2 – x + 1 = 0
(e) x 2 – x – 3 = 0
15. Assuming the graph of y = x 2 – 8x – 7 has been drawn; find the equation of the line
which should be drawn to solve the equations:
7
(a) x = 8 + (b) 2x 2 = 16x + 9
x
(c) x 2 = 7 (d) x =
4
x 8
(e)
14
2x – 5 = . x
16. Draw the graph of y = x 2 + 4x + 5 for -6 ≤ x ≤ 1. Draw suitable straight lines to find
approximate solutions of the equations:
(a) x 2 + 3x – 1 = 0 (b) x 2 + 5x + 2 = 0
17. Draw the graph of y = 2 + 3x – 2x 2 for -2 ≤ x ≤ 4.