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3 years ago

6

A transformation T: (x, y) (x - 5, y + 3).

1 answer:

aleksandrvk [35]3 years ago

8 0

The first coordinate is given the letter x and the second coordinate is given the letter y. Thus, we have that we need to substitute in the formula of the transformation 2 for x and -1 for y. Hence, we have that the image of A is given by: T(A)= (2-5, -1+3)= (-3, 2).

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3 years ago

The function f(x)=x^2 -6x+3 is transformed such that g(x)=f(x-2). Find the vertex of g(x).

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$g(x) = (x-2)^2 -6(x-2) +3$

$g(x) = x^2 -4x +4 -6x +12 +3$

$g(x) = x^2 -10 x +19$

$g(x) = x^2 -10 x + 25 +19 -25$

$g(x) = (x-5)^2 -6$

$y= (x-h)^2 -kk$

Where h,k represent the vertex and we got:

$(h,k)= (5,6)$

(5,6)

Step-by-step explanation:

We have this original function given :

$f(x) = x^2 -6x +3$

And we want to find the vertex for this new function $g(x) = f(x-2)$ and we have:

$g(x) = (x-2)^2 -6(x-2) +3$

And solving the square we got:

$g(x) = x^2 -4x +4 -6x +12 +3$

And adding similar terms we got:

$g(x) = x^2 -10 x +19$

Now we can complete the square like this:

$g(x) = x^2 -10 x + 25 +19 -25$

$g(x) = (x-5)^2 -6$

The general equation is given by:

$y= (x-h)^2 -kk$

Where h,k represent the vertex and we got:

$(h,k)= (5,6)$

(5,6)

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4 years ago