Question

The graph of $f\left(x\right)=-x^2+x-2$ is

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

The given polynomial $f\left(x\right)=-x^2+x-2$ compairing it with $f\left(x\right)=a{x}^2+bx+c$
We have
$a=-1,b=1,c=-2$
$\therefore D=1^2-4\cdot (-2)\cdot (-1)=-7\Rightarrow D<0$
Hence, roots are not real.
Thus, graph will not intersect with $x-$ axis and the graph of $y=f\left(x\right)$ will be downward parabola as $a<0$ and intersect the $y-$axis at $(0,-2)$ because $c=-2$

Now, the coordinates of vertex is $(-\frac{b}{2a},-\frac{D}{4a})$
$\Rightarrow -\frac{b}{2a}=\frac{1}{2},-\frac{D}{4a}=-\frac{7}{4}$
$\therefore (-\frac{b}{2a},-\frac{D}{4a})\equiv (\frac{1}{2},-\frac{7}{4})$
Therefore, graph will be