Question

Which of the following is/ are not a graph of quadratic?
(a)

(b)

(c)

(d)

Answer 1

Hint: For solving this problem, we consider all the options one by one and check whether they represent a quadratic graph or not. A quadratic graph can be intersecting the x-axis at two points (two distinct roots), intersecting the x-axis at one point (two equal roots) or not intersecting x axis (unreal roots). By using this methodology, we proceed to solve the problem.

Complete Step-by-Step solution:
According to the problem statement, we are given four graphs in four options and we are required to identify the graph which is not representing a quadratic polynomial.
By using the explanation provided in the hint, we proceed by:
Considering option (a), the graph does not intersect the x-axis, so it could represent quadratic polynomials having unreal roots.
Considering option (b), the graph touches the x-axis at one point, so it could represent a quadratic polynomial having two equal roots.
Considering option (c), the graph intersects the x-axis at two distinct points, so it could represent a quadratic polynomial having two distinct roots.
Considering option (d), the graph intersects the x axis at three points, so it is a cubic polynomial having three distinct roots.
Therefore, option (d) is correct.

Note: Students must be careful while observing all the graphs and must not tick mark option (a) as the graph does not intersect the x axis. They must consider all the cases possible for quadratic polynomials. Alternatively, by directly looking at the option (d), we can mark the answer without checking all the other options.