Answer
$2\text{ $x$-intercepts}$
Work Step by Step
Using $y=ax^2+bx+c,$ the given equation,
\begin{align*}
y=-2x^2+3x-1
,\end{align*} has $a=
-2
,$ $b=
3
,$ and $c=
-1
$
Using the Discriminant Formula which is given by $b^2-4ac,$ the value of the discriminant is
\begin{array}{l}\require{cancel}
&
3^2-4(-2)(-1)
\\&=
9-8
\\&=
1
\end{array}
Since the discriminant is greater than $0,$ then there are $
2
$ real solutions. With $
2
$ real solutions, then the graph of the given equation has $
2\text{ $x$-intercepts}
.$
