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Question

Select the correct graph of the quadratic polynomial y=x2x+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=x2x+2
On comparing with standard form of quadratic expression y=ax2+bx+c
we get, a=1,b=1,c=2 and D=b24ac=(1)24.(1).(2)=9
Here, D>0 therefore x2x+2=0 have two real and distinct roots.
y=x2x+2=0
x2+x2=0
x2+2xx2=0
x(x+2)1(x+2)=0
(x1)(x+2)=0
x= 1,2
From this we can say that parabola cuts the xaxis at 1 and 2 at (1,0) and (2,0).
Hence the correct graph is:



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