Answer
The graph of $f(x)=x^2+12x+36$ has one $x-$intercept.
Work Step by Step
The given function is
$\Rightarrow f(x)=x^2+12x+36$
Find the number of real solutions of $0=x^2+12x+36$
$= b^2-4ac$
Substitute $1$ for $a,12$ for $b,$ and $36$ for $c$.
$= (12)^2-4(1)(36)$
Simplify.
$= 144-144$
Subtract.
$= 0$
Discriminant is equal to $0$,
Hence, the equation has one real solutions.
The graph of $f(x)=x^2+12x+36$ has one $x-$intercept.
