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Question: Sketch the graph of y > x2 - 3x - 3 and determine whether point (5, 2) is a solution or not of the inequality.



A ) Graph 1; point (5, 2) is not a solution
B ) Graph 2; point (5, 2) is a solution
C ) Graph 3; point (5, 2) is not a solution
D ) Graph 4; point (5, 2) is a solution

Steps to derive

1 The equation corresponds to the inequality is y = x2 - 3x - 3.

2 Draw the graph of the equation and plot the point (5, 2) on the same graph.
 [Use dashed line if the inequality contains the symbol ' > '.]


3 y > x2 - 3x - 3
 [Original Inequality.]

4 2 > (5)2 - 3(5) - 3
2 > 7, which is not true.
 [Replace x with 5 and y with 2 in the inequality and simplify.]

5 The point (5, 2) is not a solution to the inequality and shade the region not containing the point as shown below.


6 The graph matches with the Graph 3 and the point (5, 2) is not a solution of the inequality.



Hence the right answer is Option C

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