1. The problem is to understand the vertex form of a quadratic function, which is given by the formula: $$y = a(x - h)^2 + k$$ 2. In this formula, $a$ controls the width and direction of the parabola (if $a > 0$, it opens upwards; if $a < 0$, it opens downwards). 3. The point $(h, k)$ is the vertex of the parabola, which is the highest or lowest point depending on the sign of $a$. 4. To graph or analyze this function, you can start by plotting the vertex at $(h, k)$. 5. Then, use the value of $a$ to determine how the parabola opens and how wide it is. 6. This form is useful for easily identifying the vertex and understanding the shape of the parabola without needing to complete the square or use the quadratic formula. Final answer: The vertex form of a quadratic function is $$y = a(x - h)^2 + k$$ where $(h, k)$ is the vertex and $a$ determines the parabola's direction and width.