Answer
$\text{no $x$-intercept}$
Work Step by Step
Using $y=ax^2+bx+c,$ the given equation,
\begin{align*}
y=7x^2-2x+9
,\end{align*} has $a=
7
,$ $b=
-2
,$ and $c=
9
.$
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(7)(9)
\\&=
4-252
\\&=
-248
\end{array}
Since the discriminant is less than $0,$ then there is no real solution. With no real solution, then the graph of the given equation has $
\text{no $x$-intercept}
.$
