What are the coordinates of the minimum point of s(x)=x+4−−−−√s(x)=x+4?

A.(4, 0)(4, 0)

B.(0, 4)(0, 4)

C.(−4, 0)(−4, 0)

D.(0, −4)(0, −4)


The function provided is \( s(x) = \sqrt{x + 4} \). To find the coordinates of the minimum point of this function, we need to analyze the behavior of \( s(x) \).

### Step 1: Determine the domain of the function
The expression inside the square root, \( x + 4 \), must be non-negative:
\[
x + 4 \geq 0
\]
\[
x \geq -4
\]
So, the domain of the function is \( x \geq -4 \).

### Step 2: Analyze the function's behavior
The square root function \( \sqrt{x} \) is increasing for \( x \geq 0 \), which means \( s(x) = \sqrt{x + 4} \) will also be increasing for \( x \geq -4 \).

### Step 3: Find the minimum point
Since the function is increasing, the minimum value occurs at the leftmost point in the domain, which is \( x = -4 \).

\[
s(-4) = \sqrt{-4 + 4} = \sqrt{0} = 0
\]

So, the minimum point of the function \( s(x) \) is at \( (-4, 0) \).

### Conclusion:
The correct answer is:
**C. \((-4, 0)\)**

Would you like more details or have any other questions?

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**Related Questions:**

1. What is the domain of the function \( f(x) = \sqrt{x + 7} \)?
2. How do you find the maximum value of a quadratic function?
3. What is the range of the function \( s(x) = \sqrt{x + 4} \)?
4. How does shifting a function horizontally affect its graph?
5. What are the coordinates of the minimum point for \( f(x) = \sqrt{x - 2} \)?

**Tip:** When finding the minimum or maximum points of a function, always consider the domain of the function first.

Learn how to find the coordinates of the minimum point for the square root function \( s(x) = \sqrt{x + 4} \). This problem involves analyzing the behavior of the square root function and determining the minimum value. Suitable for students in Grades 10-12.

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