Answer
The graph of $y=-6x^2+3x-4$ has no $x-$intercepts.
Work Step by Step
The given function is
$\Rightarrow y=-6x^2+3x-4$
Find the number of real solutions of $0=-6x^2+3x-4$
$= b^2-4ac$
Substitute $-6$ for $a,3$ for $b,$ and $-4$ for $c$.
$= (3)^2-4(-6)(-4)$
Simplify.
$= 9-96$
Subtract.
$= -87$
Discriminant is less than $0$,
Hence, the equation has no real solutions.
The graph of $y=-6x^2+3x-4$ has no $x-$intercepts.
