(a) Copy and complete the table of values for the relation \(y = -x^{2} + x + 2; -3 \leq x \leq 3\).
x
-3
-2
-1
0
1
2
3
y
-4
2
-4
(b) Using scales of 2 cm to 1 unit on the x- axis and 2 cm to 2 units on the y- axis, draw a graph of the relation \(y = -x^{2} + x + 2\). (c) From the graph, find the : (i) minimum value of y ; (ii) roots of equation \(x^{2} - x - 2 = 0\) ; (iii) gradient of the curve at x = -0.5.
Explanation
(a)
x
-3
-2
-1
0
1
2
3
y
-10
-4
0
2
2
0
-4
(b) (c) (ii) roots of the equation : \(x^{2} - x - 2 = 0\) are x = -1 or x = 2. (iii) gradient of the curve at x = -0.5 is 2.1.
