The table below is for the relation \(y = 2 + x - x^{2}\)
x
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
3
y
-4
-1.75
0
1.25
2
2.25
2
1.25
0
-1.75
-4
(a) Using a scale of 2cm to 1 unit on each axis, draw the graph of the relation in the interval \(-2 \leq x \leq 3\). (b) From your graph, find the greatest value of y and the value of x for which this occurs. (c) Using the same scale and axes, draw the graph of \(y = 1 - x\) (d) Use your graphs to solve the equation \(1 + 2x - x^{2} = 0\)
Explanation
(a) (b) The greatest value of y = 2.25 and this occurs at x = 0.5. (c) Table of values of \(y = 1 - x\)
x
-2
2
y
3
-1
(d) \(1 + 2x - x^{2} = 0\) \(1 + 1 + 2x - x - x^{2} = 1 - x\) \(2 + x - x^{2} = 1 - x\) The solution of \(1 + 2x - x^{2} = 0\) occurs at the point of intersection of \(y = 2 + x - x^{2}\) and \(y = 1 - x\). This is at points A (x = -0.8) and B (x = 2.8).
