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.