https://file.aiquickdraw.com/mathbot/file/1726980366298yl7cxeb1.jpg

The graph shows a downward-opening parabola, indicating that the coefficient of the \(x^2\) term must be negative. From the given equations, the options with a negative coefficient for \(x^2\) are:

1. \( y = -2x^2 - 2x - 3.5 \)
2. \( y = -2x^2 - 2x - 3 \)

Next, let's determine which equation best fits the vertex and y-intercept visible on the graph:

- **Vertex**: The graph has its vertex between \(x = 0\) and \(x = 1\).
- **Y-Intercept**: The y-intercept appears to be near \(-3\).

The equation \( y = -2x^2 - 2x - 3 \) has a y-intercept exactly at \(-3\), which matches the graph closely. The alternative equation \( y = -2x^2 - 2x - 3.5 \) has a y-intercept at \(-3.5\), which does not fit as well.

Therefore, the correct answer is:

\[
\boxed{y = -2x^2 - 2x - 3}
\]

Would you like a deeper explanation, or do you have any other questions?

### Related Questions:
1. How can you determine the vertex of a parabola given its equation?
2. What effect does changing the coefficient of the \(x^2\) term have on the shape of the parabola?
3. How does the constant term in a quadratic equation affect the graph?
4. What are the steps to find the axis of symmetry of a parabola?
5. How can you find the x-intercepts of a parabola algebraically?

### Tip:
When matching a graph to an equation, check key features like direction (up/down), vertex, and intercepts to identify the correct match easily.

Which equation best matches the graph shown below?

Learn how to match a quadratic equation to its graph by analyzing the direction of the parabola and identifying its vertex and intercepts. This problem focuses on selecting the equation of a downward-opening parabola with key features, suitable for students in Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation