The shape is bounded by the lines y = -x², y = 4x + 4, and y = -4x + 4. Calculate the area of the shape. Draw the figure.

Here is the graph showing the area bounded by the parabola \( y = -x^2 \), and the lines \( y = 4x + 4 \) and \( y = -4x + 4 \). The yellow shaded region represents the calculated area, which is approximately \( 5.33 \) square units.

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Here are some related questions that you might find interesting:

1. How would the area change if the parabola opened upwards instead?
2. What happens if the lines were shifted vertically? How would that affect the area?
3. How can we find the volume of a solid formed by revolving this region around the x-axis?
4. How would the area be affected if the slopes of the lines were different?
5. Can we use polar coordinates to solve similar bounded regions?

**Tip:** When dealing with intersections, sketching the graph helps visualize and set up the correct integrals!

Learn how to calculate the area bounded by the parabola y = -x² and the lines y = 4x + 4, y = -4x + 4. This problem involves finding the intersection points, setting up definite integrals, and applying the Fundamental Theorem of Calculus to determine the area. Suitable for students in Grades 11-12.

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