Transformations (math) helpDGven the parent function, f(x)=x^2, describe all transformations for g(x)=4(x+1)^2-3.

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

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To notice all transformations,we'll consider the parent function adn we'll identify it in the function g(x)=4(x+1)^2 - 3.

For the beginning, we'll expand the square from the expression of g(x):

g(x) = 4(x+1)^2 - 3

g(x) = 4(x^2 + 2x + 1) - 3

We'll remove the brackets:

g(x) = 4x^2 + 8x + 4 - 3

We'll combine like terms:

g(x) = 4x^2 + 8x + 1

We'll identify the parent function f(x) = x^2.

We'll apply square root both sides:

sqrt f(x) = sqrt x^2 = x

g(x) = 4f(x) + 8sqrt f(x) + 1

So, to get the function g(x), we'll follow the steps:

1) First, we'll multiply by 4, f(x):

4f(x)

2) We'll add square root of f(x), multiplied by 8:

4f(x) + 8sqrt f(x)

3) We'll add 1:

4f(x) + 8sqrt f(x) + 1

We've get the function g(x) = 4f(x) + 8sqrt f(x) + 1.

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