The easiest is sketching of all graphs including intercept values. Simultaneous solving is not recommended.

Depends on how well your visualisation of the graphs are.

For 2 and 3, they are quadratic curves centred at the y axis. 2 is u shaped with the minimum at y = 0, x = 0 , while 3 is n shaped with maximum point at x = 0, y = 1. They will 'overlap' and intersect at 2 points

4 is a straight line with y intercept of 6. Beyond the y intercept, y increases/decreases linearly with x. 4 would cut graph 2 at 2 points since graph 2 is going upward as x moves away from 0.

This is the same for 1 and 3, where 1's y intercept is -2 and below the x axis. So it would cut graph 3 at 2 points since graph 3 is moving downwards as x moves away from 0.

The slightly trickier one is option A. But that is easily solved if you equate the graphs, giving a result of x = 2 and x = 1.

It is actually quite intuitive that option E is the answer since the quadratic graph 3 is below the x axis pointing downwards ,and the linear graph 4 is much higher, with its intercept 6 units above the x axis, which suggests they are unlikely to meet.


I would say simultaneous equations should be done if you want to be absolutely sure.

And the ones given in the question are actually quite simple and can be done mentally, to determine if there are real roots or not. Complete the square if necessary (You can also check the discriminant)

To me this is much faster than drawing graphs. For graphs you will have to consider the scale to use. And you are unlikely to have graph paper for such MCQs so your drawing has to be accurate and to scale, if not it may result in an incorrect interpretation.