Question

Consider the functions listed below and select which functions have the same axis of symmetry.

A) f(x) = 2(x + 2)^2 – 2
B) g(x) = -2x^2 - 4x - 4
C) n(x) = -x^2 – 2x + 3
D) j(x) = -(x + 1)^2 – 2
E) k(x) = x^2 - 4x
F) m(x) = 2(x + 1)^2 – 2
A) A and F
B) B and E
C) C and D
D) B and F

Answer 1

Final answer:

The functions A) f(x) = 2(x + 2)^2 – 2 and F) m(x) = 2(x + 1)^2 – 2 have the same axis of symmetry. To find the axis of symmetry of a quadratic function, we need to determine the x-value of the vertex. Both functions have the form (x + p)^2, so the axis of symmetry is given by x = -p. Comparing the functions, we can see that A) has p = -2 and F) has p = -1.

Step-by-step explanation:

The functions A) f(x) = 2(x + 2)^2 – 2 and F) m(x) = 2(x + 1)^2 – 2 have the same axis of symmetry.

To determine the axis of symmetry of a quadratic function, we need to find the x-value of the vertex. The x-value of the vertex for a quadratic function in the form f(x) = a(x - h)^2 + k is given by h. In this case, both functions have the form (x + p)^2, so the axis of symmetry is given by x = -p. Comparing functions A and F, we can see that A) has p = -2 and F) has p = -1. Therefore, both A) and F) have the same axis of symmetry, which is x = 2 and x = 1, respectively.

Keywords: quadratic function, axis of symmetry, vertex