Question

Can someone please help me find the equation of the blue graph

Answer 1

Step-by-step explanation

From the graph, we see that the graph of G(x) is the graph of F(x) translated:

• 4 units to the left,

,

• 1 unit upward.

To translate the graph of F(x) a units to the right and b units upward, we apply the transformation:

`F(x)\rightarrow G(x)=F(x-a)+b.`

In our case, we have:

• F(x) = x²,

,

• a = -4 (because the translation is 4 units to the left),

,

• b = 1.

Replacing these data in the formula above, we find that the equation of G(x) is:

`G(x)=(x+4)^2+1.`Answer

B. G(x) = (x + 4)² + 1