Question

Find an equation of a square root curve of the form

= √ + that approximately contains the points
(3,7) and (6, 8)

Answer 1

y = √(5x+34)

Explanation:

The regression formula that matches a square root function to these points can be worked out by a suitable calculator. The attachments shows the points are matched exactly by the function ...

y = √(5x+34)

__

If you would like to work this by hand, you can put the (x, y) point values into the proposed equation and see what the coefficients need to be:

y = √(ax +b)

7 = √(3a +b) ⇒ 49 = 3a +b

8 = √(6a +b) ⇒ 64 = 6a +b

Subtracting the first equation from the second, gives ...

(64) -(49) = (6a +b) -(3a +b)

15 = 3a ⇒ a = 5

49 = 3(5) +b ⇒ b = 34