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This problem asks for a quadratic function, given three points: 

- \( x = 5 \), \( y = 15 \)
- \( x = 0 \), \( y = 20 \)
- \( x = 10 \), \( y = 0 \)

The general form of a quadratic function is:

\[
y = ax^2 + bx + c
\]

Let's solve step by step:

### a) Determine the function
Substitute the points into the equation to form a system of equations.

1. For \( x = 5 \) and \( y = 15 \):
   \[
   25a + 5b + c = 15
   \]
   
2. For \( x = 0 \) and \( y = 20 \):
   \[
   c = 20
   \]
   
3. For \( x = 10 \) and \( y = 0 \):
   \[
   100a + 10b + c = 0
   \]
   
Since \( c = 20 \), substitute this into the other two equations:

1. \( 25a + 5b + 20 = 15 \Rightarrow 25a + 5b = -5 \)
   
2. \( 100a + 10b + 20 = 0 \Rightarrow 100a + 10b = -20 \)

Now, solve this system of equations:

1. \( 25a + 5b = -5 \)
2. \( 100a + 10b = -20 \)

Divide the second equation by 2:

\[
50a + 5b = -10
\]

Now subtract the first equation from this:

\[
(50a + 5b) - (25a + 5b) = -10 - (-5)
\]
\[
25a = -5
\]
\[
a = -\frac{1}{5}
\]

Now substitute \( a = -\frac{1}{5} \) into \( 25a + 5b = -5 \):

\[
25\left(-\frac{1}{5}\right) + 5b = -5
\]
\[
-5 + 5b = -5
\]
\[
5b = 0 \Rightarrow b = 0
\]

Thus, the quadratic function is:

\[
y = -\frac{1}{5}x^2 + 20
\]

### b) What is the value of \( x \) when \( y \) is maximum?
For a quadratic function \( y = ax^2 + bx + c \), the vertex (maximum or minimum point) is given by \( x = -\frac{b}{2a} \).

Since \( b = 0 \), the vertex occurs at \( x = 0 \).

### c) What is the value of \( x \) when \( x = y \)?
Set \( y = x \) in the quadratic equation:

\[
x = -\frac{1}{5}x^2 + 20
\]

Multiply everything by 5 to eliminate the fraction:

\[
5x = -x^2 + 100
\]
\[
x^2 + 5x - 100 = 0
\]

Solve this quadratic equation using the quadratic formula:

\[
x = \frac{-5 \pm \sqrt{5^2 - 4(1)(-100)}}{2(1)}
\]
\[
x = \frac{-5 \pm \sqrt{25 + 400}}{2}
\]
\[
x = \frac{-5 \pm \sqrt{425}}{2}
\]
\[
x = \frac{-5 \pm 20.62}{2}
\]

So, the solutions are:

\[
x_1 = \frac{-5 + 20.62}{2} = 7.81 \quad \text{and} \quad x_2 = \frac{-5 - 20.62}{2} = -12.81
\]

### d) Graph the function
The quadratic function is \( y = -\frac{1}{5}x^2 + 20 \). It is an upside-down parabola with a maximum at \( (0, 20) \) and intersects the x-axis at approximately \( x = -10 \) and \( x = 10 \).

Would you like a detailed plot of this function or further clarification?

---

Here are 5 additional related questions:

1. How does changing the coefficient \( a \) in a quadratic function affect its graph?
2. How would you find the roots of a quadratic function using factoring instead of the quadratic formula?
3. What is the significance of the vertex in a quadratic function?
4. How do you calculate the discriminant of a quadratic equation, and what does it tell you about the solutions?
5. What happens to the quadratic function if the constant \( c \) is increased or decreased?

**Tip:** Always check whether the parabola opens upwards or downwards by inspecting the sign of the coefficient \( a \). A negative \( a \) indicates it opens downwards (maximum point), and a positive \( a \) means it opens upwards (minimum point).

Suatu fungsi pola kuadratik dengan informasi:
- Bila x = 5 maka y = 15
- Bila x = 0 maka y = 20
- Bila x = 10 maka y = 0

Ditanyakan:
  a) Tentukan fungsinya
  b) Berapa nilai x agar y maksimum?
  c) Berapa nilai x agar x = y
  d) Gambar fungsinya

Learn to determine a quadratic function passing through three points (x = 5, y = 15), (x = 0, y = 20), and (x = 10, y = 0). Includes steps to find maximum y, values of x for x = y, and graphing the function. Suitable for Grades 9-11.

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