https://file.aiquickdraw.com/mathbot/file/17284829587313igvkvec.jpg

The given quadratic function is of the form:

\[
f(x) = a(x - h)^2 + k
\]

We need to determine whether each constant \( a, h, \) and \( k \) is positive, negative, or zero by analyzing the graph.

### Analysis:

1. **Determining \( a \)**:
   - The value of \( a \) controls the direction of the parabola's opening. If \( a > 0 \), the parabola opens upwards. If \( a < 0 \), it opens downwards.
   - In the graph provided, the parabola opens **downwards**, indicating that \( a \) is **negative**.

2. **Determining \( h \)**:
   - The value of \( h \) is the x-coordinate of the vertex of the parabola.
   - From the graph, the vertex is on the **right side** of the y-axis, meaning \( h > 0 \). Hence, \( h \) is **positive**.

3. **Determining \( k \)**:
   - The value of \( k \) is the y-coordinate of the vertex.
   - The vertex is below the x-axis, indicating \( k < 0 \). Thus, \( k \) is **negative**.

### Final Answers:
- \( a \) is **negative**.
- \( h \) is **positive**.
- \( k \) is **negative**.

Let me know if you'd like more details or have any questions!

### Related Questions:
1. How does changing \( a \) affect the shape and width of the parabola?
2. What is the effect of \( h \) on the horizontal position of the vertex?
3. How does \( k \) influence the vertical translation of the graph?
4. What happens if \( a = 0 \)? How would the graph look?
5. How can we find the axis of symmetry using \( h \)?

**Tip**: For any quadratic function in vertex form, the vertex is located at \( (h, k) \).

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

Analyze the quadratic function f(x) = a(x - h)^2 + k based on a graph. Determine whether the constants a, h, and k are positive, negative, or zero by analyzing the parabola's direction and vertex. This problem covers key algebraic concepts for Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation