Answer
The graph of $y=-x^2+x-6$ has no $x-$intercepts.
Work Step by Step
The given function is
$\Rightarrow y=-x^2+x-6$
Find the number of real solutions of $0=-x^2+x-6$
$= b^2-4ac$
Substitute $-1$ for $a,1$ for $b,$ and $-6$ for $c$.
$= (1)^2-4(-1)(-6)$
Simplify.
$= 1-24$
Subtract.
$= -23$
Discriminant is less than $0$,
Hence, the equation has no real solutions.
The graph of $y=-x^2+x-6$ has no $x-$intercepts.
