Answer
The graph of $y=-x^2+x-6$ has one $x-$intercept.
Work Step by Step
The given function is
$\Rightarrow y=-x^2+6x-9$
Find the number of real solutions of $0=-x^2+6x-9$
$= b^2-4ac$
Substitute $-1$ for $a,6$ for $b,$ and $-9$ for $c$.
$= (6)^2-4(-1)(-9)$
Simplify.
$= 36-36$
Subtract.
$= 0$
Discriminant is equal to $0$,
Hence, the equation has one real solution.
The graph of $y=-x^2+x-6$ has one $x-$intercept.
