https://file.aiquickdraw.com/mathbot/file/1726709822061nyzdy6gc.jpg

The question in the image asks:

"Fungsi kuadrat \( f(x) = ax^2 + bx + c \) memiliki puncak di titik (2,3), jika \( a = 1 \), berapa nilai \( c \)?"

This is asking for the value of \( c \) in the quadratic function where:

- The vertex (puncak) of the parabola is given as \( (2,3) \).
- The coefficient \( a = 1 \).

### Step-by-step solution:

The general form of a quadratic function is:

\[
f(x) = ax^2 + bx + c
\]

Given the vertex is \( (2,3) \), we know that the function achieves a maximum or minimum (depending on the sign of \( a \)) at \( x = 2 \). The value of the function at this point is \( f(2) = 3 \).

We can use the vertex form of a quadratic equation:

\[
f(x) = a(x - h)^2 + k
\]

Where \( (h, k) \) is the vertex. Plugging in the values:

\[
f(x) = 1(x - 2)^2 + 3
\]

Expanding this expression:

\[
f(x) = (x - 2)^2 + 3 = (x^2 - 4x + 4) + 3 = x^2 - 4x + 7
\]

Now, comparing this to the standard form \( f(x) = ax^2 + bx + c \), we get:

- \( a = 1 \)
- \( b = -4 \)
- \( c = 7 \)

Thus, the value of \( c \) is **7**.

Would you like more details or have further questions?

### Here are 5 related questions:
1. How do you find the vertex of a quadratic function from its general form?
2. What is the importance of the coefficient \( a \) in determining the shape of the parabola?
3. Can you derive the formula for the axis of symmetry of a quadratic function?
4. How do you convert a quadratic function from vertex form to general form?
5. What is the significance of the discriminant in quadratic equations?

### Tip:
When solving quadratic functions, the vertex form \( f(x) = a(x - h)^2 + k \) is very useful for identifying the vertex directly from the equation.

Fungsi kuadrat f(x) = ax^2 + bx + c memiliki puncak di titik (2,3), jika a = 1, berapa nilai c?

This problem helps you find the value of c in a quadratic function f(x) = ax^2 + bx + c, where the vertex is at (2,3) and a = 1. Learn the vertex form of a quadratic equation and how to convert it to the standard form for solving. Suitable for students in Grades 9-11.

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