(a) Copy and complete the following table of values for \(y = 2x^{2} - 9x - 1\).
x
-1
0
1
2
3
4
5
6
y
-1
-8
-11
17
(b) Using a scale of 2cm to represent 1 unit on the x- axis and 2cm to represent 5 units on the y- axis, draw the graph of \(y = 2x^{2} - 9x - 1\).
(c) Use your graph to find the : (i) roots of the equation \(2x^{2} - 9x = 4\), correct to one decimal place ; (ii) gradient of the curve \(y = 2x^{2} - 9x - 1\) at x = 3.
Verified Correct Answer: .
Step-by-Step Mathematical Solution
(a)
x
-1
0
1
2
3
4
5
6
y
10
-1
-8
-11
-10
-5
4
17
(b)
(c)(i) \(2x^{2} - 9x = 4\)
\(2x^{2} - 9x - 1 = 4 - 1 = 3\)
At y = 3, x = 0.2 and 4.3.
(ii) Gradient of \(y = 2x^{2} - 9x - 1\) at x = 3
= \(\frac{BC}{AB} = \frac{9.5}{4.3}\)
= \(2.2\)
Source: Myschool Past Questions Archive (Record #54558)