https://file.aiquickdraw.com/mathbot/file/1727269329336q7dbqck7.jpg

From the image and the problem provided, the equation of the bird's flight trajectory is given as:

\[
f(x) = -x^2 + 4x
\]

This is a quadratic function representing a parabola, where \( f(x) \) represents the height of the bird at a given horizontal distance \( x \) from the origin. The problem asks to find the height of the bird when it reaches the cage, which is located at \( x = 2 \) meters.

Let's compute the height of the bird by substituting \( x = 2 \) into the equation.

\[
f(2) = -(2)^2 + 4(2) = -4 + 8 = 4
\]

So, the height of the bird when it reaches the cage is **4 meters**.

Would you like more details or further clarification?

Here are 5 additional related questions for practice:

1. What is the maximum height reached by the bird?
2. At what distance from the origin does the bird reach its maximum height?
3. If the bird were to land at \(x = 4\) meters, what would its height be?
4. How would the equation change if the bird flew along a wider parabola?
5. What would the equation be if the bird's path were mirrored horizontally?

**Tip:** For quadratic functions, the maximum or minimum height occurs at the vertex of the parabola, which can be calculated using \(x = -\frac{b}{2a}\) for functions of the form \(ax^2 + bx + c\).

Amatilah arah terbang dua ekor burung menuju sangkar dari arah yang berbeda. Jika jejak kedua burung terbang tersebut identik dengan f(x) = -x^2 + 4x. Lintasan jarak parabola kedua ekor burung semakin dekat ke sangkar adalah 2 meter. Tinggi burung pada saat tiba dalam sangkar adalah... meter

Solve a quadratic equation representing the flight path of two birds as they approach a cage. Learn how to compute the height of the bird when it reaches the cage, using the equation f(x) = -x^2 + 4x, and explore related quadratic function concepts.

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