Answer
$1\text{ $x$-intercept}$
Work Step by Step
Using $y=ax^2+bx+c,$ the given equation,
\begin{align*}
y=0.25x^2+2x+4
,\end{align*} has $a=
0.25
,$ $b=
2
,$ and $c=
4
.$
Using the Discriminant Formula which is given by $b^2-4ac,$ the value of the discriminant is
\begin{array}{l}\require{cancel}
&
2^2-4(0.25)(4)
\\&=
4-4
\\&=
0
\end{array}
Since the discriminant is equal to $0,$ then there is $
1
$ real solution. With $
1
$ real solution, then the graph of the given equation has $
1\text{ $x$-intercept}
.$