Question

Which function has a minimum and is transformed to the right and down from the parent function, f(x) = x2?

g(x) = –9(x2 + 2x + 1) – 7
g(x) = 4(x2 – 6x + 9) + 1
g(x) = –3(x2 – 8x + 16) – 6
g(x) = 8(x2 – 6x + 9) – 5

Answer 1

Functions B) and D) have a minimum. Other two have a maximum.
1st function: g(x)=4( x²- 6 x+9 )+1= 4( x - 3 )² +1  - it is transformed to the right and up from the parent function.
2nd function g(x)=8 ( x²  - 6 x + 9 ) -5 = 8 ( x - 3 )² - 5 - it is transformed to the right and down.
Answer: D) 

Answer 2

The function that has a minimum and is transformed to the right and down from the parent function is; g(x) = 8(x² - 6x + 9 ) - 5

How to Interpret Functions?

By inspection, only Functions B) and D) have a minimum.

For the first function in option B, we have:

g(x) = 4(x²- 6x + 9) + 1

This can be simplified to;

g(x) = 4( x - 3 )² + 1

Thus, we can say that this first function is transformed to the right and up from the parent function.

For the second function in option D, we have;

g(x) = 8(x² - 6x + 9 ) - 5

The function can be simplified to get;

g(x) = 8( x - 3 )² - 5

Thus, we can say that it is transformed to the right and down.

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