The graphs below have the same shape. What is the equation of the blue
graph?
G(x) =
A. G(x) = (x + 3)2-5
B. G(x) = (x+3)2 +5
C. G(x) = (x - 3)2 + 5
D. G(x) = (x - 3)2-5

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:

The

equationof thetranslatedfunction is:g(x) = (x + 3)^2 - 2

## How to get the equation for the blue graph?

We can see that the

bluegraph is a translation of theredone, where theequationfor the redgraphis:f(x) = x^2

Rememberthat thetranslationsare:Horizontal translation:

For a

generalfunction f(x), ahorizontaltranslation of N units iswrittenas:g(x) = f(x + N).

If

Nispositive, theshiftis to theleft.If

Nisnegative, theshiftis to theright.Vertical translation:

For a

generalfunction f(x), averticaltranslation of N units iswrittenas:g(x) = f(x) + N.

If

Nispositive, the shift isupwards.If

Nisnegative, the shift isdownwards.By

analyzingthe vertices, we can see that thevertexof the blue graph is at (-3, -2) so we have atranslationof 3 units to the left and2 unitsdown,meaningthat wehave:g(x) = f(x + 3) - 2 = (x + 3)^2 - 2

So the

correctoption isA.If you want to learn more about

translations, you can read:brainacademy.pro/question/11468584

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