Final answer:
To find the square root function, the general form f(x) = a√(x - h) + k is used with the starting point (-1, 6) leading to f(x) = a√(x + 1) + 6. Using another point (3, 16), the parameter 'a' is found to be 5, giving the equation of the function as f(x) = 5√(x + 1) + 6.
Step-by-step explanation:
To find the equation of a square root function that starts at (-1, 6) and passes through (3, 16), we need to establish a general form of the function and then use the given points to find the specific parameters.
A square root function generally has the form:
f(x) = a√(x - h) + k
Where (h, k) is the starting point, and 'a' is a scaling factor.
Using the starting point (-1, 6), our function takes the form:
f(x) = a√(x + 1) + 6
Now, using the point (3, 16) to solve for 'a':
f(3) = a√(3 + 1) + 6 = 16
a√4 + 6 = 16
2a + 6 = 16
2a = 10
a = 5
Therefore, the equation of the square root function is:
f(x) = 5√(x + 1) + 6