The given quadratic function is expressed in vertex form:

$f(x) = a(x - h)^2 + k$

From the image, we need to determine the signs (positive, negative, or zero) of the constants $a$, $h$, and $k$ based on the graph.

Analyzing the graph:

1. The parabola opens upward, which means the value of $a$ must be positive. When $a > 0$, the parabola opens upward, and when $a < 0$, it opens downward.
2. The vertex of the parabola seems to be to the right of the y-axis, indicating that $h$ (the x-coordinate of the vertex) is positive.
3. The vertex of the parabola is below the x-axis, meaning that the value of $k$ (the y-coordinate of the vertex) is negative.

Summary:

• $a$ is positive.
• $h$ is positive.
• $k$ is negative.

Would you like more details or have any specific questions on this?

Here are some related questions:

1. What is the significance of the parameter $a$ in a quadratic function?
2. How does the value of $h$ affect the graph of a quadratic function?
3. How does the value of $k$ determine the vertex's position relative to the x-axis?
4. What happens to the graph when $a$ becomes negative?
5. Can a parabola's vertex lie on the y-axis? What would $h$ be in that case?

Tip: The vertex form of a quadratic equation is useful for easily identifying the vertex of the parabola, given by the point $(h, k)$.