Can't values A and B that will make function pass through points. (Please see image)

[bratch]

Hello, I'm having a problem solving a problem in Ivan Savov's 'No BS Guide to Math and Physics' book. Part of my problem is that I am not entirely sure if the number 2 before the square root is indicating 2 multiplied by the root or that it is a SQUARE root. However I have tried solving the problem on both scenarios but I still cannot figure out the value for

and

for the life of me. The entire problem is written below and attached on an image.

E.1.21: Find the values [imath]A[/imath] and [imath] B[/imath] that will make the function [imath]g(x) = 2sqrt(x-A) + B[/imath] pass through points (3, -2), (4, 0), (7, 2)

The answer is: A = 3, B= -2

As I mentioned, the 2 before the square root sign is not clear to me if it's multiplying the root or indicating it's a square root. If anyone can help me I would greatly appreciate it!

 

[BigBeachBanana]

The 2 before the square root is multiplication. It's a system of equations with 2 unknowns, but since they gave you 3 points, you'll have 3 equations, but you only need 2 of the 3 to solve for A and B. Pick any 2 that you prefer, and solve them simultaneously.
[math] -2=2\sqrt{3+A}+B\\ 0=2\sqrt{4+A}+B\\ 2=2\sqrt{7+A}+B\\ [/math]Also, the answer should be A=-3 and B=-2.

 

[topsquark]

Hello, I'm having a problem solving a problem in Ivan Savov's 'No BS Guide to Math and Physics' book. Part of my problem is that I am not entirely sure if the number 2 before the square root is indicating 2 multiplied by the root or that it is a SQUARE root. However I have tried solving the problem on both scenarios but I still cannot figure out the value for

and

for the life of me. The entire problem is written below and attached on an image.

E.1.21: Find the values [imath]A[/imath] and [imath] B[/imath] that will make the function [imath]g(x) = 2sqrt(x-A) + B[/imath] pass through points (3, -2), (4, 0), (7, 2)

The answer is: A = 3, B= -2

As I mentioned, the 2 before the square root sign is not clear to me if it's multiplying the root or indicating it's a square root. If anyone can help me I would greatly appreciate it!

Symbolically the degree of the root will be a superscript: [imath]\sqrt[n]{x}[/imath] so if the number is in the line like it is ([imath]n \sqrt{x}[/imath] ) then it is a multiplication.

-Dan

 

[bratch]

The 2 before the square root is multiplication. It's a system of equations with 2 unknowns, but since they gave you 3 points, you'll have 3 equations, but you only need 2 of the 3 to solve for A and B. Pick any 2 that you prefer, and solve them simultaneously.
[math] -2=2\sqrt{3+A}+B\\ 0=2\sqrt{4+A}+B\\ 2=2\sqrt{7+A}+B\\ [/math]Also, the answer should be A=-3 and B=-2.

Thank you, I was way over complicating it!

 

[Steven G]

If that 2 was associated with the sqrt sign, then how would you denote that you were multiplying a sqrt by 2??