Answer
$(4,32)$
Work Step by Step
A point is on the graph of $y=3x^2-8\sqrt{x}$ if its $x$ and $y$ coordinates satisfy the equation.
To know this, substitute the $x$ and $y$ coordinates of each point into the equation to obtain:
For $(-1,-5)$:
$y=3x^2 - 8\sqrt x$
$-5\ne3(-1)^2 -8\sqrt -1$
For $(4,32)$:
$y=3x^2 - 8\sqrt x$
$32=3(4)^2 - 8\sqrt 4$
$32=48-16$
$32=32 : \checkmark$
For $(9,171)$:
$y=3x^2 - 8\sqrt x$
$171=3(9)^2 - 8\sqrt 9$
$171=243-24$
$171\ne219 $
Thus, the only point that is on the graph of $y=3x^2-8\sqrt{x}$ is $(4, 32)$.
