HOW TO WRITE THE EQUATION OF A SQUARE ROOT FUNCTION FROM A GRAPH

Problem 1 :

Solution:

By observing the graph (0, -3) is (h, k).

General equation of the square root function is

y = a√(x - h) + k

y = a√(x - 0) - 3

The curve passing through the point (1, -2).

-2 = a√(1 - 0) - 3

-2 = a√1 - 3

-2 = a - 3

a = 1

By applying the value a = 1 in above equation 

y = 1√(x - 0) - 3

y = √x - 3

f(x) = √x - 3

Problem 2 :

Solution:

By observing the graph (-3, 0) is (h, k).

General equation of the square root function is

y = a√(x - h) + k

y = a√(x + 3) + 0

The curve passing through the point (-2, 1).

1 = a√(-2 + 3) + 0

1 = a√1  

a = 1

By applying the value a = 1 in above equation 

y = 1√(x + 3) + 0

y = √(x + 3)

f(x) = √(x + 3)

Problem 3 :

Solution:

By observing the graph (3, 3) is (h, k).

General equation of the square root function is

y = a√(x - h) + k

y = a√(x - 3) + 3

The curve passing through the point (4, 4).

4 = a√(4 - 3) + 3

4 = a√1 + 3

a = 1

By applying the value a = 1 in above equation 

y = 1√(x - 3) + 3

y = √(x - 3) + 3

f(x) = √(x - 3) + 3

Problem 4 :

Solution:

By observing the graph (0, 3) is (h, k).

General equation of the square root function is

y = a√(x - h) + k

y = a√(x - 0) + 3

The curve passing through the point (1, 4).

4 = a√(1 - 0) + 3

4 = a√1 + 3  

a = 1

By applying the value a = 1 in above equation 

y = 1√(x - 0) + 3

y = √x + 3

f(x) = √x + 3

Problem 5 :

Solution:

By observing the graph (-3, -3) is (h, k).

General equation of the square root function is

y = a√(x - h) + k

y = a√(x + 3) - 3

The curve passing through the point (-2, -2).

-2 = a√(-2 + 3) - 3

-2 = a√1 - 3  

a = 1

By applying the value a = 1 in above equation 

y = 1√(x + 3) - 3

y = √(x + 3) - 3

f(x) = √(x + 3) - 3

Problem 6 :

Solution:

By observing the graph (3, 0) is (h, k).

General equation of the square root function is

y = a√(x - h) + k

y = a√(x - 3) + 0

The curve passing through the point (4, 1).

1 = a√(4 - 3) + 0

1 = a√1   

a = 1

By applying the value a = 1 in above equation 

y = 1√(x - 3) + 0

y = √(x - 3) 

f(x) = √(x - 3)