Question

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Answer 1

The equation in the vertex form of g(x) is:

$g(x) = (x + 1)^2 - 38$

How to get the equation of function g?

We know that g(x) is a translation of 2 units below and 3 units to the left of f(x).

So first, let's rewrite f(x) to its vertex form:

$f(x) = x^2 - 4x - 32$

The vertex is at:

$x = -(-4)/2*1 = 2$

The y-value of the vertex is:

$f(2) = 2^2 - 4*2 - 32 = -36$

Then the vertex form of f(x) is:

$f(x) = (x - 2)^2 - 36$

If we move this vertex 2 units below, and 3 units to the left, then we have:

$g(x) = f(x +3) - 2\\\\g(x) = (x - 2 + 3)^2 - 36 - 2\\\\g(x) = (x + 1)^2 - 38$

That is the equation for g(x) in vertex form.

If you want to learn more about quadratic equations:

brainly.com/question/1214333

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