The equation of the translated function is:
g(x) = (x + 3)^2 - 2
How to get the equation for the blue graph?
We can see that the blue graph is a translation of the red one, where the equation for the red graph is:
f(x) = x^2
Remember that the translations are:
Horizontal translation:
For a general function f(x), a horizontal translation of N units is written as:
g(x) = f(x + N).
If N is positive, the shift is to the left.
If N is negative, the shift is to the right.
Vertical translation:
For a general function f(x), a vertical translation of N units is written as:
g(x) = f(x) + N.
If N is positive, the shift is upwards.
If N is negative, the shift is downwards.
By analyzing the vertices, we can see that the vertex of the blue graph is at (-3, -2) so we have a translation of 3 units to the left and 2 units down, meaning that we have:
g(x) = f(x + 3) - 2 = (x + 3)^2 - 2
So the correct option is A.
If you want to learn more about translations, you can read:
brainly.com/question/11468584
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