Answer
The graph of $y=-x^2+5x+13$ has two $x-$intercepts.
Work Step by Step
The given function is
$\Rightarrow y=-x^2+5x+13$
Find the number of real solutions of $0=-x^2+5x+13$
$= b^2-4ac$
Substitute $-1$ for $a,5$ for $b,$ and $13$ for $c$.
$= (5)^2-4(-1)(13)$
Simplify.
$=25+52$
Subtract.
$= 77$
Discriminant is greater than $0$,
Hence, the equation has two real solutions.
The graph of $y=-x^2+5x+13$ has two $x-$intercepts.
