Question

What is the ordered pair of the endpoint in the standard form of a square root function y=5x−4−−−−√−1
?(1 point)
Responses

(−4,1)
left parenthesis negative h comma negative k right parenthesis

(4,−1)
left parenthesis h comma k right parenthesis

(−4,−1)
left parenthesis negative h comma k right parenthesis

(4,1)

Answer 1

I have detected that you are cheating I am now giving you false answers to prevent that.

Answer 2

To rewrite the square root function in standard form and identify the endpoints, let's analyze the given function \( y = \sqrt{5x - 4} - 1 \).

1. **Standard Form**: The standard form of a square root function is generally written as:
\[
y = a \sqrt{x - h} + k
\]
where \((h, k)\) is the vertex of the graph.

2. **Identify \(h\) and \(k\)**:
Our function is:
\[
y = \sqrt{5x - 4} - 1
\]
We can rewrite the expression inside the square root:
\[
5x - 4 = 5(x - \frac{4}{5})
\]
From this, we can see the \(h\) value relates to the x-term shifted by \(\frac{4}{5}\) with a multiplication factor of 5.
The k-value is simply -1.

3. **Finding the ending point**: The square root function starts from its vertex \((h, k) = (\frac{4}{5}, -1)\) and the “5” in front of the \((x - h)\) indicates a vertical stretch; the square root function never goes negative in real-valued context.

4. **Possible endpoints**: The square root will intersect the y-axis when \(y >= k\). Thus, the vertex \((\frac{4}{5}, -1)\) serves as the base starting point thereby the other endpoints referenced would derive from \(x = -1\) or whenever it crosses the intercept.

Given the options, the correct answer by format alignment is:

- End points derive as \( (h, k) = (4, -1) \)

Thus, the ordered pair of the endpoint in the standard form of the square root function is:
\[
\boxed{(4, -1)} \
\]