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Misha Larkins [42]
3 years ago
10

Function g can be thought of as a translation (shifted) version of f(x)=x^2

Mathematics
1 answer:
Natasha_Volkova [10]3 years ago
8 0

Answer:

Step-by-step explanation:

f(x)=x^2  represents a parabola with vertex at (0, 0), that opens up.

If we translate this graph h units to the right, then g(x) will be:

g(x) = (x - h)^2.

If we translate the graph of  f(x)=x^2 k units up, then g(x) will be:

f(x)=x^2 + k

Next time, please indicate whether you are shifting the original graph to the right or to the left, and/or up or down.

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  1. 6x +y = -6
  2. 6x -y = 8
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Step-by-step explanation:

To rewrite these equations from point-slope form to standard form, you can do the following:

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Of course, any operation you do must be done <em>to both sides of the equation</em>.

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1. y -6 = -6(x +2)

  y -6 = -6x -12 . . . . . eliminate parentheses

  6x +y -6 = -12 . . . . . add 6x

  6x +y = -6 . . . . . . . . add 6

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2. y +2 = 6(x -1)

  y +2 = 6x -6

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  -6x +y = -8

  6x -y = 8 . . . . . . . . multiply by -1

__

3. y -3 = -5(x -2)

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_____

<em>Additional comment</em>

The "standard form" of a linear equation is ax+by=c for integers a, b, c. The leading coefficient (generally, 'a') should be positive, and all coefficients should be mutually prime (have no common factors). That is why we multiply by -1 in problem 2.

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