Question

The graphs below have the same shape. f(x) = x2
What is the equation of the graph of g(x)?

Answer 1

The answer is C. g(x) = (x - 2)²

This is because when translating a shape in the x-axis, the signs change. This means that when the graph moves to the right by 2 units, you write it as (x - 2)² instead of (x + 2)². Also, when dealing with translations in the x-axis they must be represented in the brackets, so (x - 2)² as opposed to x² - 2.

You can check that this is true, and also confirm that other answers are false, by substituting in a value of x from the g(x) graph and seeing if it produces the correct y-value. For example, when x = 2, y = 0, so if we substitute x = 2 into each option we get:

A. g(2) = (2 + 2)² = 4² = 16

B. g(2) = (2)² + 2 = 4 + 2 = 6

C. g(2) = (2 - 2)² = 0

D. g(2) = (2)² - 2 = 4 - 2 = 2

I hope this helps! Let me know if you have any questions :)

Answer 2

g(x)=(x-2)^2

Explanation:

the equation of of the graph of g(x) is:

g(x)=(x-2)^2, since the following transformation has been done to it:

right one unit

since the equation in vertex form is g(x)=a(x-h)^2+k, it is moved two units to the right and not to the left

since g(x) has the same shape, it had not been compressed or stretched by any means, meaning that a is 1