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Which is one of the transformations applied to the graph of f(x) = x2 to change it into the graph of g(x) = 4x2 + 24x + 30?

The graph of f(x) = x2 is widened.
The graph of f(x) = x2 is shifted left 3 units.
The graph of f(x) = x2 is shifted up 30 units.
The graph of f(x) = x2 is reflected over the x-axis.

Respuesta :

Changing g(x) to this form: a(x-h) + k, we have:
g(x) = 4 (x+3)^2 - 6

Comparing this to the original equation, f(x) = x^2, we have the following transformations:

The graph is widened.
The graph is shifted left 3 units.

Using translation concepts, it is found that the correct option is given by:

The graph of f(x) = x² is shifted left 3 units.

What is a translation?

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

In this problem, we have that the original function is:

f(x) = x².

The translated function is:

g(x) = 4x² + 24x + 30.

Factoring it we have that:

g(x) = 4(x² + 6x + 7.5) = 4[(x + 3)² - 1.5].

Since x -> x + 3, the function was shifted left 3 units.

More can be learned about translation concepts at https://brainly.com/question/4521517

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