Question: Sketch the graph of y ≥ x2 - 4x and find the quadrant in which the obtained graph lies.
A ) Only on 1st quadrant
B ) All the quadrants
C ) Only on 2nd, 3rd and 4th quadrants
D ) Only on 1st, 2nd and 4th quadrants
Steps to derive
[Original quadratic inequality.]
1 y ≥ x2 - 4x
2 Taking different values of x and calculating y values from the quadratic inequality y ≥ x2 - 4x, a graph is obtained as shown below.
3 From the graph, it can be concluded that the graph is in 1st, 2nd and 4th quadrants.
4 The graph of the inequality y ≥ x2 - 4x lies in 1st, 2nd and 4th quadrants.
Hence the right answer is Option D
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