State the minimum or maximum value of y and the corresponding value of x for
y=4(x^2) + 2 .
$\displaystyle y = 4(x - 0)^2 + 2$
compare your equation to the vertex form of a quadratic equation ...
$\displaystyle y = a(x - h)^2 + k$
where the vertex is the point $\displaystyle (h,k)$
since $\displaystyle a > 0$ , $\displaystyle x = h$ is the vertex location and $\displaystyle y = k$ is the corresponding minimum value