Find Intervals of Increase and Decrease: y = -4√7x² Quadratic Function

The function is given by $y = -4\sqrt{7}x^2$, which is a downward-opening parabola because the coefficient $a = -4\sqrt{7}$ is negative.

The vertex of the parabola is at the origin (0,0). A downward-opening parabola decreases as $x$ moves away from the vertex in the positive $x$-direction, and increases as $x$ moves away from the vertex in the negative $x$-direction.

Thus, the intervals of increase and decrease for this function are:

• The function increases on the interval $(-\infty, 0)$.
• The function decreases on the interval $(0, \infty)$.

Therefore, the intervals of increase and decrease can be denoted as:

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