To model the given data set with a square root function of the form [tex]\(y = a \sqrt{x - b} + c\)[/tex], we can use the provided coefficients [tex]\(a, b, c\)[/tex]. Here is the detailed explanation:
The problem asks for the model in the form:
[tex]\[ y = a \sqrt{x - b} + c \][/tex]
From the given data and calculated coefficients, we know:
1. [tex]\(a = 10.76\)[/tex]
2. [tex]\(b = 9.12\)[/tex]
3. [tex]\(c = 43.64\)[/tex]
Thus, substituting these values into the equation, we get:
[tex]\[ y = 10.76 \sqrt{x - 9.12} + 43.64 \][/tex]
So the fully formed square root function that best models the set of data is:
[tex]\[ y = 10.76 \sqrt{x - 9.12} + 43.64 \][/tex]
To match this equation with the provided mathematical expression template:
[tex]\[
y =
\underbrace{10.76}_{a}
\sqrt{
x -
\underbrace{9.12}_{b}
}
+
\underbrace{43.64}_{c}
\][/tex]
Therefore, when you drag the numbers into the correct locations, it should look like this:
[tex]\[ y = \text{10.76} \sqrt{x - \text{9.12}} + \text{43.64} \][/tex]
