Question

Select the correct graph of the quadratic polynomial $y=-x^2-x+2.$

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

Since the coefficient of $x^2$ is negative the parabola will be downward opening parabola.
Given quadratic expression: $y=-x^2-x+2$
On comparing with standard form of quadratic expression $\text{y}=a{x}^2+bx+c$
we get, $a=-1,b=-1,c=2$ and $D=b^2-4ac=(-1{)}^2-4.(-1).(2)=9$
Here, $D>0$ therefore $-x^2-x+2=0$ have two real and distinct roots.
$\Rightarrow y=-x^2-x+2=0$
$\Rightarrow x^2+x-2=0$
$\Rightarrow x^2+2x-x-2=0$
$\Rightarrow x(x+2)-1(x+2)=0$
$\Rightarrow (x-1)(x+2)=0$
$\Rightarrow x=1,-2$
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: