What is -7(x-2)=1=15-7x

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Step-by-step explanation:

Simplifying

-7(x + -2) + 1 = 15 + -7x

Reorder the terms:

-7(-2 + x) + 1 = 15 + -7x

(-2 * -7 + x * -7) + 1 = 15 + -7x

(14 + -7x) + 1 = 15 + -7x

Reorder the terms:

14 + 1 + -7x = 15 + -7x

Combine like terms: 14 + 1 = 15

15 + -7x = 15 + -7x

Add '-15' to each side of the equation.

15 + -15 + -7x = 15 + -15 + -7x

Combine like terms: 15 + -15 = 0

0 + -7x = 15 + -15 + -7x

-7x = 15 + -15 + -7x

Combine like terms: 15 + -15 = 0

-7x = 0 + -7x

-7x = -7x

Add '7x' to each side of the equation.

-7x + 7x = -7x + 7x

Combine like terms: -7x + 7x = 0

0 = -7x + 7x

Combine like terms: -7x + 7x = 0

0 = 0

Solving

0 = 0

Couldn't find a variable to solve for.

This equation is an identity, all real numbers are solutions.

Step-by-step explanation:

The transformation to the parent quadratic function can be described either of two ways. For a quadratic, a vertical stretch can also be accomplished by a horizontal compression.

The transformations of interest here are ...

  g(x) = a·f(x) . . . . vertical stretch by a factor of 'a'

  g(x) = f(a·x) . . . . horizontal compression by a factor of 'a'

  g(x) = f(x) +a . . . . vertical translation by 'a' units

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It is easy to see that the parent function f(x) = x^2 has had 9 added to it, so the function has been translated upward 9 units.

The transformation to 3x^2 can be accomplished either of two ways:

  3x^2 = 3(x^2) . . . vertical stretch by a factor of 3

  3x^2 = (x√3)^2 . . . . horizontal compression by a factor of √3

The attached graph shows either a horizontal compression or a vertical stretch will result in the same graph.

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Additional comment

In the interest of using rational scale factors, we prefer the "vertical stretch, vertical up" description.