DESCRIBE THE TRANSFORMATIONS OF THE QUADRATIC FUNCTIONS GIVEN

Describe the transformation of f(x) = x² represented by g. Then graph each function.

Problem 1 :

g(x) = x² − 3

Solution :

Parent function :

f(x) = x²

Compare with f(x) = a (x - h)² + k

Transformed function :

g(x) = x² − 3

k = -3, so we move the graph 3 units down.

Problem 2 :

g(x) = x² + 1

Solution :

Parent function :

f(x) = x²

Compare with f(x) = a (x - h)² + k

Transformed function :

g(x) = x² + 1

k = 1, so we move the graph 1 unit up.

Problem 3 :

g(x) = (x + 2)²

Solution :

Parent function :

f(x) = x²

Compare with f(x) = a (x - h)² + k

Transformed function :

g(x) = (x + 2)²

g(x) = (x - (-2))²

h = -2, so we move the graph 2 unit left.

Problem 4 :

g(x) = (x + 6)² − 2

Solution :

Parent function :

f(x) = x²

Compare with f(x) = a (x - h)² + k

Transformed function :

g(x) = (x + 6)² − 2

g(x) = (x - (-6))² − 2

Here h = -6 and k = -2

So, we move the graph 6 units left and 2 units down.

Problem 5 :

g(x) = -x²

Solution :

Parent function :

f(x) = x²

Compare with f(x) = a (x - h)² + k

Transformed function :

g(x) = -x²

Reflection across y-axis.

Problem 6 :

g(x) = (1/2) (x − 1)²

Solution :

Vertical shrink by the factor of 1/2 followed by translation of 1 unit left.

Problem 7 :

g(x) = (x - 2)² − 8

Solution :

Horizontal translation 2 units left and 8 units down.