Square root graph: ‘Pointed’ or ‘Rounded’ at X-intercept (9740 syllabus only)

Square root graph can appear as ‘Pointed’ or ‘Rounded’ at the X-intercept.

The shape depends whether the original point on X-axis is a stationary point.

square root theory

Example 1

sq1

2

x=-3 is a stationary point. Therefore, the square root graph at x=-3 will be pointed.

x= 2 is not a stationary point. Therefore, the square root graph at x= 2 will be rounded.

Example 2

ex2

To determine the shape of the square root graph at the x-intercept, we can use GC to determine the gradient.

1

Therefore, the first graph at x=1 appears as two oblique tangents while the second graph at x=1 is flat.

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