Question

Jonathan graphed a square root function. What is the equation of the function Jonathan graphed? The equation y=1/2square root of x- blank the graph shows a curved line that starts at 4 on the x axis and goes 5, 6, 7, 8

Answer 1

To find the equation of the square root function that Jonathan graphed, we need to analyze the given information. The given equation is in the form:

\[ y = \frac{1}{2} \sqrt{x} - \text{(some value)} \]

From your description, it seems that the graph starts at \( x = 4 \) and potentially goes up to \( 5, 6, 7, 8 \) on the y-axis.

To determine the missing value in the equation, we can substitute \( x = 4 \) into the equation to see what would be needed for \( y = 0 \), assuming that the graph starts from the x-axis (where \( y=0 \)):

1. Plugging \( x = 4 \) into the equation:
\[
y = \frac{1}{2} \sqrt{4} - b
\]
where \( b \) is the blank we need to fill.

2. Since \( \sqrt{4} = 2 \), this simplifies to:
\[
y = \frac{1}{2} \times 2 - b = 1 - b
\]

3. If the graph starts at \( y = 0 \) when \( x = 4 \):
\[
0 = 1 - b
\]
This means:
\[
b = 1
\]

Putting everything together, the equation of the function Jonathan graphed is:

\[ y = \frac{1}{2} \sqrt{x} - 1 \]

This function has a starting point on the x-axis (where \( y = 0 \)) at \( x = 4 \). As \( x \) increases beyond 4, the value of \( y \) will increase as well.