Hi taureanamir,

Quantity B can be rewritten as y as \(2s-s^2\) =\(y(s)\). Now from the figure t < y as point (s,t) is inside the parabola and x-axis.

Hence B is greater.

PS: Please share the source of the question.

Regards
_________________

Thank you very much Sandy.

The question is from a local institute's book.

Could you please elaborate on the solution a little.

Could you please make it more clear by elaborate?

They say pictures are worth a 1000 words.




So you have been given an equation of parabola you can use the value of x coordinate to calculate the y coordinate. If you see the picture above it becomes clear why B is greater.
_________________

Hey there, I solved it a little differently. First found the vertex (1, 1): x coordinate of the vertex = -b/2a. Then plug in x and solve for y, which will give you the (x,y) coordinate of the vertex. In this case it is (1,1).


Since the point (s, t) is below the vertex (1,1), s<1 and t<1. From here I just picked a number that satisfied s<1 and t<1 and solved. It worked; there may be a better way to do this, but hope this helps a little.

There is a different way to solve this:

Let's assume there is a point on the parabola directly above the given point. The x coordinate will remain the same that is s. But the y coordinate will be something like t+c, where c is a positive number. So the coordinates of the point should be (s,t+c).

As this point is on the parabola it should satisfy the equation of the parabola so, plugin the values. It gives us t+c=2s-s2. Therefore if we subtract c from both sides we can see that t is c less than 2s-s2, as c is a positive number. So B is the correct choice.

Thanks for this explanation. I now understand that the question does not even need you to perform any calculation.

s=x at the same point of the parabola but from the position it is less than y in the equation of the parabola.

Since s=x is constant and t is less than y, then B is the answer.