Answer
$2\text{ $x$-intercepts}$
Work Step by Step
Using $y=ax^2+bx+c,$ the given equation,
\begin{align*}
y=10x^2+13x-3
,\end{align*} has $a=
10
,$ $b=
13
,$ and $c=
-3
.$ Using the Discriminant Formula which is given by $b^2-4ac,$ the value of the discriminant is
\begin{array}{l}\require{cancel}
&
13^2-4(10)(-3)
\\&=
169+120
\\&=
289
\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}
.$
