Find Intervals of Increase and Decrease for y = 3√5x²

Let's solve the problem:

The given function is $y = 3\sqrt{5}x^2$. This is a quadratic function in standard form with $a = 3\sqrt{5}$, which is positive. Quadratics with positive coefficients open upwards and have a distinctive symmetry:

• The interval of decrease: $x < 0$ because the function decreases as we move left from the vertex at the origin.
• The interval of increase: $x > 0$ because the function increases as we move right from the vertex at the origin.

This matches the mathematical property of parabolas where $a > 0$: they decrease until the vertex and then increase past the vertex.

Thus, the intervals of increase and decrease for the function $y = 3\sqrt{5}x^2$ are:

$\searrow:x<0\\\nearrow:x>0$