https://file.aiquickdraw.com/mathbot/file/1727220392932l3j00fji.jpg

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 \((h, k)\).

From the graph of the quadratic function given by f(x) = a(x - h)^2 + k, determine whether each constant a, h, and k is positive, negative, or zero.

Analyze the graph of a quadratic function given in vertex form f(x) = a(x - h)^2 + k to determine whether the constants a, h, and k are positive, negative, or zero. Learn how the parabola's direction and position relate to the values of a, h, and k. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation