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Sonbull [250]
3 years ago
6

The parent function f(x) = x^2 is vertically stretched by a scale factor of 2, translated 14 units right, and 6 units up. Which

equation below represents the new equation? 1. G(x) = 2(x-14)^2 + 6 2. G(x) = 1/2 (x-14)^2 = 6 3. G(x) = 2(x-14)^2 - 6 4. G(x) = 2(x+14)^2 + 6
Mathematics
1 answer:
Elena-2011 [213]3 years ago
4 0

Answer:

(1)\; G(x)=2(x-14)^2+6

Step-by-step explanation:

Assuming, right and up are positive directions.

The given parent function, f(x)=x^2

Let f_1(x) be the function when the parent function is stretched by a scale factor of 2.

So, f_1(x)=2f(x)

\Rightarrow f_1(x)=2x^2

Let f_2(x) be the function when f_1(x) is translated 14 units right.

So, f_2(x)=f_1(x-14)

\Rightarrow f_2(x)=2(x-14)^2

Again, let f_3(x) be the function when f_2(x) is translated 4 units up.

So, f_3(x)=f_2(x)+6

\Rightarrow f_3(x)=2(x-14)^2+6

So, the resulting function, f_3(x)=G(x)=2(x-14)^2+6.

Hence, option (1) is correct.

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