what are the different graph and plots for quadratic equations in certain condition like a>0, D<0.(somethings like a parabola without open side, toching x axis etc)

what are the number and nature of roots and what do these graphs tell us about the equations.

Also, please suggest any book, pdf or website where i can get these graphs. Currently i have Higher Algerbra by Hall & Knight which does not have these graphs.

Dear Ashu,

In mathematics, a quadratic equation is a univariate polynomial equation of the second degree. A general quadratic equation can be written in the form

where x represents a variable or an unknown, and a, b, and c are constants with a ≠ 0. (If a = 0, the equation is a linear equation.)

The constants a, b, and c are called respectively, the quadratic coefficient, the linear coefficient and the constant term or free term. The term "quadratic" comes from quadratus, which is the Latin word for "square". Quadratic equations can be solved by factoring, completing the square, graphing, Newtons method, and using the quadratic formula 

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