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Question

Select the correct graph of the quadratic polynomial y=âˆ’x2âˆ’x+2.

A
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B
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C
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D
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Solution

The correct option is A Since the coefficient of x2 is negative the parabola will be downward opening parabola. Given quadratic expression: y=−x2−x+2 On comparing with standard form of quadratic expression y=ax2+bx+c we get, a=−1,b=−1,c=2 and D=b2−4ac=(−1)2−4.(−1).(2)=9 Here, D>0 therefore −x2−x+2=0 have two real and distinct roots. ⇒y=−x2−x+2=0 ⇒x2+x−2=0 ⇒x2+2x−x−2=0 ⇒x(x+2)−1(x+2)=0 ⇒(x−1)(x+2)=0 ⇒x= 1,−2 From this we can say that parabola cuts the x−axis at 1 and −2 at (1,0) and (−2,0). Hence the correct graph is:

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