Answer
$2\text{ $x$-intercepts}$
Work Step by Step
Using $y=ax^2+bx+c,$ the given equation,
\begin{align*}
y=x^2+17x-2
,\end{align*} has $a=
1
,$ $b=
17
,$ and $c=
-2
.$
Using the Discriminant Formula which is given by $b^2-4ac,$ the value of the discriminant is
\begin{array}{l}\require{cancel}
&
17^2-4(1)(-2)
\\&=
289+8
\\&=
297
\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}
.$
