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Question: The graphs of the given pair of functions intersect. Calculate their points of intersection algebraically.
y = x2 - 9
y = 4x2 - 30x - 9


A ) (0, - 9) and (- 10, 91)
B ) (0, 9) and (10, - 91)
C ) (0, - 9) and (10, 91)
D ) (0, - 9) and (- 10, - 91)

Steps to derive

1 y = x2 - 9
 [Equation 1.]

2 y = 4x2 - 30x - 9
 [Equation 2.]

3 x2 - 9 = 4x2 - 30x - 9
 [Equating (1) and (2).]

4 x2 - 9 - 4x2 + 30x + 9 = 0
 [Collect all the terms on one side.]

5 - 3x2 + 30x + 0 = 0
Þ - 3x2 + 30x = 0
 [Factor.]

6 - 3x(x - 10) = 0
 [Factor.]

7 Þ - 3x = 0 or x - 10 = 0
 [Evaluate.]

8 Þ x = 0 or x = 10
 [Evaluate.]

9 When x = 0:
y = (0)2 - 9 = - 9
When x = 10:
y = (10)2 - 9 = 91
 [Substitute the values.]

10 So, the points of intersection of the given two graphs are (0, - 9) and (10, 91).



Hence the right answer is Option C

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