https://file.aiquickdraw.com/mathbot/file/1726187493135yhms0tx0.jpg

The problem provides a quadratic function \( f(x) = 10 - x^2 \) and asks to identify the correct transformed function \( y = 4f(x) \) among the options.

### Step-by-Step Solution:

1. **Original Function:**
   \[
   f(x) = 10 - x^2
   \]
   
2. **Transformation:**
   The question asks for \( y = 4f(x) \), which means multiplying the function \( f(x) \) by 4:
   \[
   y = 4 \cdot (10 - x^2) = 4 \cdot 10 - 4 \cdot x^2 = 40 - 4x^2
   \]

3. **Conclusion:**
   The transformed function is \( y = 40 - 4x^2 \), which matches option **D**.

Thus, the correct answer is **D**.

Let me know if you have any further questions or want more details.

### Follow-up Questions:
1. How do you graph a quadratic function like \( 10 - x^2 \)?
2. What is the effect of multiplying a quadratic function by a constant like 4?
3. Can you find the vertex of the original function \( f(x) = 10 - x^2 \)?
4. How do transformations affect the graph of a function?
5. Can we use this method to solve other types of function transformations?

### Tip:
Always apply transformations step by step, starting with the basic function before applying any scaling or shifts.

Diketahui fungsi kuadrat f(x) = 10 - x^2. Gambarlah grafik fungsi berikut berdasarkan y = 4f(x)

Explore how to graph a quadratic function f(x) = 10 - x^2 and apply transformations to find the correct function y = 4f(x). This problem includes multiplying functions by constants and analyzing quadratic transformations. Suitable for high school students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation