# What Transformations Change the Graph of f(x) to the Graph of g(x)? f(x) = x^{2}, g(x) = (x + 5)^{2} - 9

We will be using the formula of transformations to solve this.

## Answer: If f(x) = x^{2}, g(x) = (x + 5)^{2} - 9, then the transformations from f(x) to g(x) is 5 units to the left and 9 units down.

Let's solve this step by step.

**Explanation:**

Given that, f(x) = x^{2}, g(x) = (x + 5)^{2} - 9

We have general formula of transformations as f(x) = a(bx − h)^{n} + k

Here, k is the vertical shift, h is the horizontal shift, a is the vertical stretch and b is the horizontal stretch.

On comparing g(x) with the general formula of transformations, we get h = -5 and k = -9

⇒ The negative sign indicates that the graph has shifted 5 units to the left and 9 units down.

### Hence, if f(x) = x^{2}, g(x) = (x + 5)^{2} - 9, then the transformations from f(x) to g(x) is 5 units to the left and 9 units down.

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