so if the parabola is -3x, it is concave down but shuld the parabola get narrower or fatter

If the equation of the parabola is \( y = -3x^2 \), then the parabola will be **concave down** (opening downward) because the coefficient of \( x^2 \) is negative.

### Width of the Parabola:
- The coefficient here is \( -3 \), and since \( |a| = 3 \), which is greater than 1, the parabola will be **narrower** than the standard parabola \( y = -x^2 \) or \( y = x^2 \).

In summary, the parabola \( y = -3x^2 \) is **concave down** and **narrower** compared to the standard parabola \( y = x^2 \).

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### Related Questions:
1. How does the constant \( c \) in the equation \( y = ax^2 + bx + c \) affect the graph of the parabola?
2. How can you determine the vertex of the parabola \( y = -3x^2 + bx + c \)?
3. What is the axis of symmetry for the parabola \( y = -3x^2 + bx + c \)?
4. How does the value of \( b \) affect the direction and position of the parabola?
5. What is the effect of the coefficient \( a \) on the focus and directrix of a parabola?

### Tip:
Always check the sign of the coefficient of \( x^2 \) to determine the direction the parabola opens, and its magnitude to determine how wide or narrow it is.

Explore how the parabola -3x^2 behaves, including its concavity and width. Learn about the effect of the coefficient -3 on the parabola's shape and size. Suitable for high school students studying quadratic equations and parabolas.

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