(a) Copy and complete the table of values for y = 2x\(^{2}\) + x - 10 for -5 \(\leq\) x \(\leq\) 4.
x
-5
-4
-3
-2
-1
0
1
2
3
4
y
5
-9
-10
0
(b) Using scales of 2cm to 1 unit on the x- axis and 2cm to 5 units on the y- axis, Draw the graph of y = 2x\(^{2}\) + x - 10 for -5 \(\leq\) x \(\leq\) 4.
(c) Use the graph to find the solution of :
(i) 2x\(^{2}\) + x = 10
(ii) 2x\(^{2}\) + x - 10 = 2x
Verified Correct Answer: .
Step-by-Step Mathematical Solution
(a)
x
-5
-4
-3
-2
-1
0
1
2
3
4
y
35
18
5
-4
-9
-10
-7
0
11
26
(b)
(c)(i) 2x\(^{2}\) + x = 10 \(\equiv\) 2x\(^{2}\) + x - 10 = 0
Thus, the solution of 2x\(^{2}\) + x - 10 = 0 are the values of x at which the curve cuts the x- axis.
x = -2.5 or x = 2.
(ii) 2x\(^{2}\) + x - 10 = 2x
To solve the given equation, we first draw the graph of y = 2x: when x = -2, y = 2(-2) = -4; when x = 3, y = 2(3) = 6.
The values of x at which y = 2x\(^{2}\) + x - 10 and y = 2x intersect give the solution of 2x\(^{2}\) + x - 10 = 2x.
These are x = -2 or x = 2.5.
Source: Myschool Past Questions Archive (Record #52316)