The following is an incomplete table for the relation \(y = 2x^{2} - 5x + 1\)
x
-3
-2
-1
0
1
2
3
4
5
y
8
1
-1
26
(a) Copy and complete the table. (b) Using a scale of 2cm to 1 unit on the x- axis and 2cm to 10 units on the y- axis, draw the graph of the relation \(y = 2x^{2} - 5x + 1\) for \(-3 \leq x \leq 5\). (c) Using the same scale and axes, draw the graph of \(y = x + 6\). (d) Estimate from your graphs, correct to one decimal place : (i) the least value of y and the value of x for which it occurs ; (ii) the solution of the equation \(2x^{2} - 5x + 1 = x + 6\).
Explanation
(a) \(y = 2x^{2} - 5x + 1\)
x
-3
-2
-1
0
1
2
3
4
5
y
34
19
8
1
-2
-1
4
13
26
Table of value for \(y = x + 6\)
x
-2
0
2
y
4
6
8
(b) (d) (i) Least value of y = -2 occurs at x = 1 (ii) Solution of \(2x^{2} - 5x + 1 = x + 6\) are x = -0.7 and x = 3.7.
