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**ibdutt** y = ax^2+bx + c ------- (1)

It is given the x intercept is . That means when y = 0 x = 1

Hence from ( 1 ) we get a + b + c = 0 ----- ( 2 )

Again we have y intercept = -3. That means when x = 0 y = -3.

Again from (1) we get c = -3. ------- ( 3 )

Now it says that the slope of tangent is 1 at y intercept. It means slope of tangent = 1 at ( 0,-3)

But the slope of tangent to a curve is given by dy/dx. Thus fro ( 1)

dy/dx = 2ax + b at ( 0,-3 ), dy/dx = 1. Thus we have b = 1 ----- ( 4 )

Now from (1), (2) and (3) we get a = 2, b=1 and c = -3.

Thus by plugging in these values in (1) we get the function as

2x^2 + x – 3 = 0