Describe the transformation of f(x) = x^{2} represented by g. Then graph each function.
Problem 1 :
g(x) = x^{2} − 3
Solution :
Parent function :
f(x) = x^{2}
Compare with f(x) = a (x - h)^{2} + k
Transformed function :
g(x) = x^{2} − 3
k = -3, so we move the graph 3 units down.
Problem 2 :
g(x) = x^{2} + 1
Solution :
Parent function :
f(x) = x^{2}
Compare with f(x) = a (x - h)^{2} + k
Transformed function :
g(x) = x^{2} + 1
k = 1, so we move the graph 1 unit up.
Problem 3 :
g(x) = (x + 2)^{2}
Solution :
Parent function :
f(x) = x^{2}
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) = x^{2}
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) = -x^{2}
Solution :
Parent function :
f(x) = x^{2}
Compare with f(x) = a (x - h)^{2} + k
Transformed function :
g(x) = -x^{2}
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.
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM