Question

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

Answer 1

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.