(a) Copy and complete the following table of values for the relation \(y = 2x^{2} - 7x - 3\).
x
-2
-1
0
1
2
3
4
5
y
19
-3
-9
(b) Using 2 cm to 1 unit on the x- axis and 2 cm to 5 units on the y- axis, draw the graph of \(y = 2x^{2} - 7x - 3\) for \(-2 \leq x \leq 5\).
(c) From your graph, find the : (i) minimum value of y ;
(ii) gradient of the curve at x = 1.
(d) By drawing a suitable straight line, find the values of x for which \(2x^{2} - 7x - 5 = x + 4\).
Verified Correct Answer: .
Step-by-Step Mathematical Solution
(a) \(y = 2x^{2} - 7x - 3\)
x
-2
-1
0
1
2
3
4
5
\(2x^{2}\)
8
2
0
2
8
18
32
50
\(-7x\)
14
7
0
-7
-14
-21
-28
-35
\(-3\)
-3
-3
-3
-3
-3
-3
-3
-3
\(y\)
19
6
-3
-8
-9
-6
1
12
(b)
(c)(i) Minimum value of y = -9
(ii) \(y = 2x^{2} - 7x - 3\)
Gradient = \(\frac{\mathrm d y}{\mathrm d x} = 4x - 7\)
Gradient at x = 1 : \(4(1) - 7 = 4 - 7 = -3\).
(d) \(2x^{2} - 7x - 5 = x + 4\)
\(2x^{2} - 7x - 5 + 2 = x + 4 + 2\)
\(2x^{2} - 7x - 3 = x + 6\)
\(\implies y = x + 6\)
x
-2
-1
0
1
2
3
4
5
6
6
6
6
6
6
6
6
6
y
4
5
6
7
8
9
10
11
From the graph, x = -0.9 or 5.
Source: Myschool Past Questions Archive (Record #53197)