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Question: The graphs of the given pair of functions intersect. Calculate their points of intersection algebraically.
y = 5x2 - 7
y = - x2 + 11x + 14


A ) (-76, -736) and (3, 38)
B ) (-76, -736) and (- 3, 38)
C ) (-76, -736) and (3, - 38)
D ) (76, -736) and (3, 38)

Steps to derive

1 y = 5x2 - 7
 [Equation 1.]

2 y = - x2 + 11x + 14
 [Equation 2.]

3 5x2 - 7 = - x2 + 11x + 14
 [Equating (1) and (2).]

4 5x2 - 7 + x2 - 11x - 14 = 0
 [Collect all the terms on one side.]

5 6x2 - 11x - 21 = 0
 [Group the like terms.]

6 (6x + 7)(x - 3) = 0
 [Factor.]

7 Þ 6x + 7 = 0 or x - 3 = 0
 [Use the zero-product property.]

8 Þ x = - 76 or x = 3
 [Evaluate.]

9 When x = - 76
y = 5 (- 76)2 - 7
= 5(4936) - 7
= -736
 [Simplify.]

10 When x = 3
y = 5(3)2 - 7 = 38
 [Substitute the values.]

11 So, the points of intersection of the given two graphs are (-76, -736) and (3, 38).



Hence the right answer is Option A

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