The curve `y = ax^2 + bx + c` will open downward, if :

The chord joining the points where x = p and x = q on the curve y = ax^(2)+bx+c is parallel to the tangent at the point on the curve whose abscissa is

Focus of parabola y = ax^(2) + bx + c is

The curve y=ax^2+bx +c passes through the point (1,2) and its tangent at origin is the line y=x . The area bounded by the curve, the ordinate of the curve at minima and the tangent line is

If the line y=2x touches the curve y=ax^(2)+bx+c at the point where x=1 and the curve passes through the point (-1,0), then

If graph of the quadratic y = ax ^(2)+bx+c is given below : then:

If the curve y=ax^(2)+bx+c passes through the point (1, 2) and the line y = x touches it at the origin, then

If the curve y=ax^(3) +bx^(2) +c x is inclined at 45^(@) to x-axis at (0, 0) but touches x-axis at (1, 0) , then

The tangent to y = ax ^(2)+ bx + (7 )/(2) at (1,2) is parallel to the normal at the point (-2,2) on the curve y = x ^(2)+6x+10. Then the vlaue of a/2-b is:

ax + by = c bx+ ay =1 +c