Question

The function g(x) = (x + 2)2 + 4 is a transformation of the parent function f(x) = x2. Select all the statements that are true about the transformation.
A. Function g is the result of f being translated right 2 units and down 4 units.
B. Function g is the result of f being translated left 2 units and up 4 units.
C. The graph of function f opens upward.
D. The graph of function g opens downward.
E. The graph of function f is compressed by a factor of 2.

Answer 1

Answer:

Step-by-step explanation:

B

C

Answer 2

Using translation and parabola concepts, it is found that the correct options are:

A. Function g is the result of f being translated right 2 units and down 4 units.

C. The graph of function f opens upward.

------------------------------

• The parent function is: $f(x) = x^2$
• Function g is given by: $g(x) = (x + 2)^2 + 4$
• Shifting a function f(x) a units to the right is the same as finding f(x + a).
• Shifting a function f(x) a units up is the same as finding f(x) + a.
• From the last two bullet points, option A is correct and option B is incorrect.
• In both functions, f and g, the term that multiplies $x^2$ is positive, thus, both open upward, which means that option C is correct and option D is incorrect.
• Both are multiplied by the same factor, 1, thus none are compressed, and option E is incorrect.

A similar problem is given at https://brainly.com/question/4521517