https://file.aiquickdraw.com/mathbot/file/1727993848032dp01gfnr.jpg

Let me help you break down and solve the problems from the image:

### 1. **Jika sumbu simetri suatu parabola adalah \( x = 1 \) dengan \( f(1) = -4 \) dan \( f(4) = 5 \), tentukan bentuk \( f(x) \).**

This is a quadratic function of the form \( f(x) = ax^2 + bx + c \).

Given:
- Axis of symmetry: \( x = 1 \)
- \( f(1) = -4 \) (This gives a condition for \( a \), \( b \), and \( c \))
- \( f(4) = 5 \) (Another condition to use for solving)

Let's solve this step by step.

### 2. **Seseorang membuat keripik dengan modal Rp100.000 untuk membeli peralatan membuat keripik.**
- **Biaya untuk membuat satu bungkus keripik** adalah Rp4.000.
- Let \( p \) be the price of one packet of chips, where \( p \) is in rupiah.
- The number of chips produced is given by \( q = 80 - 5p \).
  
   - **Expenses:** Total expenses include the equipment cost and production cost.
   - The **profit** is the revenue from selling chips minus the total costs.

We can define a **revenue function** and subtract the **cost function** to find profit.

### 3. **Based on question 2, determine whether the following statements are true or false:**
   1. If one packet of chips is sold at Rp7,000, total revenue is Rp315,000.
   2. If the chips are sold at Rp11,000, total revenue is Rp350,000.
   3. If one packet of chips is sold at Rp12,000, the total profit is Rp60,000.

Each of these scenarios can be solved by calculating the revenue using the functions defined in question 2.

### 4. **Draw the graphs of the following quadratic functions on a Cartesian diagram:**
   a. \( f(x) = (x + 3)^2 - 4 \)
   b. \( f(x) = x^2 + 2x + 1 \)

Here, you would plot these quadratic equations to visualize their curves.

### 5. **Determine the quadratic function passing through points (-1,0), (0,2), and (2,0).**

This can be solved by assuming the function is of the form \( f(x) = ax^2 + bx + c \) and using the points provided to form a system of equations to solve for \( a \), \( b \), and \( c \).

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Would you like to go into detail for any specific problem, or would you like me to solve a particular one? Here are 5 additional questions based on this:

1. How do you determine the vertex of a quadratic function given its standard form?
2. How would you verify whether a calculated revenue function is correct?
3. What is the significance of the axis of symmetry in quadratic functions?
4. How would you solve a system of equations for three unknowns using substitution or elimination?
5. How does the profit function change if the fixed cost (like equipment) increases?

**Tip**: When working with quadratic functions, completing the square can often reveal important properties like the vertex and axis of symmetry easily.

1. Jika sumbu simetri suatu parabola adalah x = 1 dengan f(1) = -4 dan f(4) = 5, tentukan bentuk f(x).
2. Seseorang membuat keripik dengan modal Rp100.000 untuk membeli peralatan membuat keripik. Biaya yang diperlukan untuk membuat satu bungkus keripik adalah Rp4.000. Jika p adalah harga jual keripik dalam satuan ribu rupiah, maka banyak keripik yang dibuat dirumuskan sebagai q = 80 - 5p. Tentukan fungsi total pendapatan dan keuntungan.
3. Berdasarkan soal cerita nomor 2, tentukan apakah pernyataan berikut benar atau salah.
4. Gambar grafik fungsi kuadrat berikut pada diagram Cartesius.
5. Tentukan fungsi kuadrat yang melalui titik (-1, 0), (0, 2), dan (2, 0).

Solve quadratic equations involving symmetry, revenue functions, and profit calculations for a chip-making scenario. Includes step-by-step guidance for solving equations, drawing graphs, and analyzing business profits. Ideal for students in Grades 9-12.

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