Question

Pleaseee help with this

Answer 1

Answer:

g(x) = (x + 1)^2 + 3

Step-by-step explanation:

When x is replaced by x - h, it results in a horizontal translation of h units.

When y is replaced by y - k, it results in a vertical translation of k units.

f(x) = x^2 is the original function.

Rewrite it as

y = x^2

To translate it 1 unit left, you need h = -1.

x - h = x - (-1) = x + 1. Replace x with x + 1.

Now you have y = (x + 1)^2.

To translate 3 units up, you have k = 3.

y - k = y - 3. Replace y with y - 3.

y - 3 = (x + 1)^2

Solve for y.

y = (x + 1)^2 + 3

Replace y with g(x).

g(x) = (x + 1)^2 + 3