Draw the graphs of the quadratic po...
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Draw the graphs of the quadratic polynomial f(x)=3-2x -x?

JEE/Engineering Exams
Maths
Solution
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Let ( y=f(x) ) or ( , y=3-2 x-x^{2} ) Let us list a few values of ( y=3-2 x-x^{2} ) corresponding to a few values of ( x ) as follows: begin{tabular}{|c|c|c|c|c|c|c|c|c|c|} hline ( mathrm{x} ) & -5 & -4 & -2 & -1 & 0 & 1 & 2 & 3 & 4 hline ( mathrm{y}=3-2 mathrm{x}-mathrm{x}^{2} ) & -12 & -5 & 3 & 4 & 3 & 0 & -5 & -12 & -21 hline end{tabular} Thus, the following points lie on the graph of polynomial ( y=3-2 x-x^{2}: ) [ (-5,-12),(-4,-5),(-3,0),(-2,3),(-1,4),(0,3),(1,0),(2,-5), ] (3,-12) and (4,-21) Let us plot these points on a graph paper and draw a smooth free hand curve passing through these points to obtain the graph of ( y=3-2 x-x^{2} . ) The curve thus obtained represents a parabola, as shown in figure.
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