graphs OF quadratic polynomial

Basic question on formation OF quadratic equation || 6 std. graph OF quadratic polynomial

Which of the following condition is correct for the graph of quadratic polynomial p(x) = ax^(2) + bx + c to be an upward parabola?

which one of the following can best represent the graph of quadratic polynomial y=ax^(2)+bx+c (where a 0)?

Consider the graph of quadratic polynomial y=ax^(2)+bx+c as shown below.Which of the following is/are correct?

If graph of quadratic polynomial ax ^(2)+bx+c cuts positive direction of y-axis,then what is the sign of c?

If the graph of quadratic polynomial ax^(2)+bx+c cuts negative direction of y -axis, then what is the sign of c?

State 'T' for true and 'F' for false and select the correct option. I. If a quadratic polynomial f(x) is a square of a linear polynomial, then its two zeroes are coincident. II. If a quadratic polynomial f(x) is not factorisable into linear factors, then it has no real zero. III. If graph of quadratic polynomial ax^(2)+bx+c cuts positive direction of y-axis, then the sign of c is positive. IV. If fourth degree polynomial is divided by a quadratic polynomial, then the degree of the remainder is 2.

Suppose the graph of quadratic polynomial y=x^(2)+px+q is situated so that it has two arcs lying between the rays y=x and y=2x,x>=0. These two arcs are projected onto the x-axis yielding segments S_(L) and S_(R), with S_(R) to the right of S_(L.) .Find the difference of the length l(S_(R))-l(S_(L))

Graph of quadratic polynomial when polynomial have no zeroes