(a) Draw the table of values for the relation \(y = x^{2}\) for the interval \(-3 \leq x \leq 4\). (b) Using a scale of 2 cm to 1 unit on the x- axis and 2 cm to 2 units on the y- axis, draw the graphs of : (i) \(y = x^{2}\) ; (ii) \(y = 2x + 3\) for \(-3 \leq x \leq 4\). (c) Use your graph to find : (i) the roots of the equation \(x^{2} = 2x + 3\) ; (ii) the gradient of \(y = x^{2}\) at x = -2.
Explanation
(a)
x
-3
-2
-1
0
1
2
3
4
\(y = x^{2}\)
9
4
1
0
1
4
9
16
(b) \(y = 2x + 3\)
x
-3
-2
-1
0
1
2
3
4
2x
-6
-4
-2
0
2
4
6
8
3
3
3
3
3
3
3
3
3
y
-3
-1
1
3
5
7
9
11
(c)(i) The roots of the equation are -1 and 3, from the graph. (ii) The gradient of \(y = x^{2}\) at x = -2 : \(\frac{8}{-2.5} = -3.2\)
