Question

The parent function f(x) = x2 is translated such that the function g(x) = –x2 + 6x – 5 represents the new function. What is true about the transformation that was performed?

Answer 1

Answer:

1. Translation 3 units to the right;

2. Reflection across the x-axis;

3. Translation 4 units up.

Step-by-step explanation:

First, rewrite the function $g(x)$ in following way:

$g(x)=-x^2+6x-5=-(x^2-6x)-5=-(x^2-6x+9-9)-5=-(x-3)^2+9-5=-(x-3)^2+4.$

Apply such transformations:

1. Translate the graph of the parent function $f(x)$ 3 units to the right to get the graph of the function $f_1(x)=(x-3)^2.$

2. Reflect the graph of the function $f_1(x)$ across the x-axis to get the graph of the function $f_2(x)=-(x-3)^2.$

3. Translate the graph of the function $f_2(x)$ 4 units up to get the graph of the function $g(x)=-(x-3)^2+4.$

Answer 2

Answer:

a c d

Step-by-step explanation: