Question

Which of the following functions has a graph in which the vertex and axis of symmetry are to the left of the vertex and axis of symmetry of the graph of f(x) = (x – 1)2 + 1? Select all that apply.
A. g(x) = 2(x − 1)2 − 1
B. g(x) = −(x + 1)2 − 2
C. g(x) = 2(x − 1)2 + 2
D. g(x) = −(x − 2)2 + 1
E. g(x) = −(x + 2)2 + 2
F. g(x) = 2(x + 1)2 + 2

Answer 1

Given : f(x) = (x - 1)²  + 1

To Find : graph in which the vertex and axis of symmetry are to the left of the vertex and axis of symmetry of the graph of f(x)

A. g(x) = 2(x − 1)² − 1

B. g(x) = −(x + 1)² − 2

C. g(x) = 2(x − 1)² + 2

D. g(x) = −(x − 2)² + 1

E. g(x) = −(x + 2)² + 2

F. g(x) = 2(x + 1)² + 2

Step-by-step explanation:

f(x) = (x - 1)²  + 1

Hence Vertex is (  1, 1)

Axis of symmetry is x = 1

Vertex will lie on axis of symmetry only

Hence we will check axis of symmetry only

graph in which the vertex and axis of symmetry are to the left of the vertex

Hence Axis of symmetry must be x < 1

B. g(x) = −(x + 1)² − 2        Axis of symmetry is x = -1  

E. g(x) = −(x + 2)² + 2       Axis of symmetry is x = -2

F. g(x) = 2(x + 1)² + 2       Axis of symmetry is x = -1

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Answer 2

Answer: F, E, B

Step-by-step explanation:

The axis of symmetry for the original function is 1, coming from the point (1,1) and the axis of these graphs are all under one