# What is the range of the function y = x^2?

The range is $y \ge 0$.
Normally, you would complete the square and check the leading coefficient, $a$, to determine the concavity for the comparison sign. However, this function is already in vertex or standard form:
$y = {\left(x - 0\right)}^{2} + 0$
So the vertex is $\left(0 , 0\right)$ and the leading coefficient is positive; this means the parabola is concave up and the vertex has the minimum value. The minimum value is the bottom of the range of the function.