Question: The graphs of the given pair of functions intersect. Calculate their points of intersection algebraically.
y = x2
y = (- 17)x2 + (87)x + 48
A ) (7, 49) and (- 6, - 36)
B ) (7, 49) and (- 6, 36)
C ) (7, - 49) and (- 6, 36)
D ) (7, - 49) and (6, - 36)
Steps to derive
1 y = x2
[Equation 1.]
2 y = (- 17)x2 + (87)x + 48
[Equation 2.]
3 x2 = - (17)x2 + (87)x + 48
[Equating (1) and (2).]
4 x2 + (17)x2 - (87)x - 48 = 0
[Collect all the terms on one side.]
5 7x2 + x2 - 8x - 336 = 0
[Multiply throughout by 7.]
7 8x2 - 8x - 336 = 0
[Group the like terms.]
8 8(x2 - x - 42) = 0
[Factor.]
9 x2 - x - 42 = 0
[Divide throughout by 8.]
10 (x - 7)(x + 6) = 0
[Factor.]
11 Therefore, x = 7, - 6
[Evaluate.]
12 When x = 7:
y = (7)2 = 49
13 When x = - 6:
y = (- 6)2 = 36
[Substitute the values.]
14 So, the points of intersection of the given two graphs are (7, 49) and (- 6, 36).
Hence the right answer is Option B
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