Analyze the concavity of the quadratic function $h\left(x\right)=m{x}^2+nx+p$. Determine the conditions on $m$, $n$, and $p$ for $h\left(x\right)$ to be concave up and concave down.

$h\left(x\right)$ is concave up if $m>0$ and concave down if , regardless of $n$ and $p$.

$h\left(x\right)$ is concave up if $n>0$ and concave down if , regardless of $m$ and $p$.

$h\left(x\right)$ is concave up if $p>0$ and concave down if , regardless of $m$ and $n$.

$h\left(x\right)$ is concave up if and concave down if $m>0$, regardless of $n$ and $p$.