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The given equation is:

\[
y = -\frac{1}{32}x^2 - \frac{1}{4}x - \frac{17}{2}
\]

This is a quadratic equation of the form \( y = ax^2 + bx + c \), where:

- \( a = -\frac{1}{32} \)
- \( b = -\frac{1}{4} \)
- \( c = -\frac{17}{2} \)

To determine the direction in which the parabola opens, we look at the sign of the coefficient \( a \) in front of the \( x^2 \) term.

- If \( a > 0 \), the parabola opens upwards.
- If \( a < 0 \), the parabola opens downwards.

In this case, \( a = -\frac{1}{32} \), which is negative. Therefore, the parabola opens **downwards**.

Would you like more details or have any questions?

Here are some related questions:
1. How do we find the vertex of a parabola from its equation?
2. What is the axis of symmetry for this parabola?
3. How can we determine if the parabola is wide or narrow based on the coefficient \( a \)?
4. How do we find the roots (x-intercepts) of this quadratic equation?
5. How would the graph change if the sign of \( a \) were positive?

**Tip:** The coefficient \( a \) not only determines the direction of the parabola but also affects how "steep" or "wide" the parabola appears. A smaller absolute value of \( a \) makes the parabola wider, while a larger absolute value makes it narrower.

Which direction does the parabola defined by the equation \( y = -\frac{1}{32}x^2 - \frac{1}{4}x - \frac{17}{2} \) open?

Learn how to determine the direction in which the parabola opens for the quadratic equation y = -1/32x^2 - 1/4x - 17/2. This solution covers key algebraic concepts and explains the impact of the coefficient 'a' on the parabola's direction. Suitable for students in Grades 9-10.

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