Find Intervals of Increase and Decrease for y = 4x² - 80

To determine the intervals of increase and decrease for the quadratic function $y = 4x^2 - 80$, follow this approach:

• First, identify the function's form: $y = 4x^2 - 80$, where $a = 4$, $b = 0$, and $c = -80$.
• Find the vertex $x$-coordinate using the formula $x = -\frac{b}{2a} = -\frac{0}{2 \times 4} = 0$.
• Since $a = 4$ which is positive, the parabola opens upwards.
• With the parabola opening upwards, it decreases before the vertex and increases after the vertex.
• Identify the intervals: The function decreases on the interval $x < 0$ and increases on $x > 0$. The turning point (minimum) occurs precisely at $x = 0$.

Therefore, the function decreases for $x < 0$ and increases for $x > 0$.

The intervals of increase and decrease are $\searrow: x < 0$ and $\nearrow:x > 0$.