1. The problem asks for the name of the point where a parabola changes direction. 2. In algebra and calculus, this point is known as the vertex of the parabola. 3. The vertex is the highest or lowest point on the parabola, depending on whether it opens downward or upward. 4. For a parabola given by the quadratic function $$y = ax^2 + bx + c$$, the vertex can be found using the formula for the x-coordinate: $$x = -\frac{b}{2a}$$ 5. Once the x-coordinate is found, substitute it back into the function to find the y-coordinate: $$y = a\left(-\frac{b}{2a}\right)^2 + b\left(-\frac{b}{2a}\right) + c$$ 6. This point $(x, y)$ is where the parabola changes direction, also called the turning point or vertex.