Finding Intervals of Increase and Decrease in Parabolas: Using the x² Coefficient and Vertex

To determine the intervals of increase and decrease for a parabola, we primarily rely on the coefficient of $x^2$ in the quadratic function, noted as $a$ in either the standard form $ax^2 + bx + c$ or vertex form $a(x-h)^2 + k$. The vertex of the parabola, given by $(h, k)$, plays a crucial role as the turning point.

Steps to find intervals of increase and decrease:

• Step 1: The coefficient $a$ tells us whether the parabola opens upwards ($a > 0$) or downwards ($a < 0$). A parabola opening upwards decreases to the vertex and increases thereafter, while a parabola opening downwards increases to the vertex and decreases thereafter.
• Step 2: The vertex's $x$-coordinate, $h$, provides the dividing line between these intervals. The parabola is increasing on one side and decreasing on the other.

The intervals of increase and decrease depend on both $a$ and $h$ - not $k$ alone. Therefore, knowing just the $y$-coordinate of the vertex ($k$) is insufficient to determine these intervals, as it does not influence the $x$-intercepts or the opening direction.

Conclusively, knowledge of only the coefficient $a$ and the $y$-coordinate of the vertex is insufficient to fully determine the intervals of increase and decrease of a parabola. The intervals are primarily determined by the sign of $a$ and the vertex’s $x$-coordinate.

Therefore, the correct choice is: Incorrect.