Plot a graph for the equation ` y=ax-bx^(2)` , where a and b are positive constants.

If y=a+bx^(2) , where a, b are arbitrary constants, then

The path of a projectile is given by the equation y = ax – bx^(2) , where a and b are constants and x and y are respectively horizontal and vertical distances of projectile from the point of projection. The maximum height attained by the projectile and the angle of projection are respectively.

The potential energy of a conservative is given by u = ax^2 - bx , where a and b are positive constants. Discuss whether the equilibrium is stable, Unstable or neutral.

A particle moves in the plane XY with constant accelenration a direction along the negative Y-axis . The equation of motion of the particle has the form , y = Ax - Bx^(2) . Where A and B are positive constants. Find the velcotiy of the particle at the origin of the coordinates.

If y=a+ bx^(2) , where a, b are constants, then

If y=a+ bx^(2) , where a, b are constants, then