https://file.aiquickdraw.com/mathbot/file/17269801856607w37ev6x.jpg

To determine which equation best matches the graph, we will analyze the shape and key features of the parabola.

### Observations:
1. The graph is a downward-opening parabola, meaning the coefficient of \( x^2 \) must be negative.
2. The vertex appears to be at approximately \( (0, 4) \), suggesting the y-intercept is around \( 4 \).
3. The parabola appears symmetric about the y-axis, with roots at approximately \( x = -2 \) and \( x = 2 \), implying the axis of symmetry is \( x = 0 \), which fits equations with no horizontal shift.

### Analysis of the options:
We can eliminate the positive \( x^2 \)-term equations since the parabola opens downward. The remaining two equations are:
- \( y = -0.7x^2 - x + 4 \)
- \( y = -0.7x^2 - x + 4.4 \)

### Y-intercept check:
The graph shows a y-intercept at \( y = 4 \), so the correct equation should have \( +4 \), not \( +4.4 \).

Thus, the correct answer is:
**\( y = -0.7x^2 - x + 4 \)**.

Would you like further details on this explanation?

Here are 5 follow-up questions for further practice:
1. How does the coefficient of \( x^2 \) affect the width and direction of the parabola?
2. How would the graph change if the constant term were \( +5 \) instead of \( +4 \)?
3. What effect does the \( -x \) term have on the graph’s shape?
4. How can you determine the vertex of a parabola from its equation?
5. What is the significance of the parabola's axis of symmetry?

**Tip**: To quickly identify the direction of a parabola, look at the sign of the \( x^2 \)-term. A negative sign means it opens downward, while a positive sign means it opens upward.

Which equation best matches the graph shown below?

Determine which quadratic equation matches the graph of a downward-opening parabola with vertex at (0, 4) and a y-intercept of 4. Learn to analyze quadratic functions and their graphs, suitable for students in Grades 9-11.

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