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Each statement describes a transformation of the graph of y = x2. Which statement correctly describes the graph of y = (x + 4)2 - 7?

A.
It is the graph of y = x2 translated 4 units down and 7 units to the left.

B.
It is the graph of y = x2 translated 4 units up and 7 units to the left.

C.
It is the graph of y = x2 translated 7 units down and 4 units to the left.

D.
It is the graph of y = x2 translated 7 units down and 4 units to the right.

Respuesta :

GoddessofDork
  • Vertex Form: [tex] y=(x-h)^2+k [/tex] , with (h,k) as the vertex.

So the new equation is in vertex form. And looking at this equation, we see the vertex as (-4,-7) (Remember that y = (x + 4)^2 - 7 can be also written as y = (x - (-4))^2 - 7).

Since negative x-coordinates go to the left on the x-axis and negative y-coordinates go down on the y-axis, your answer is going to be C. It is the graph of y = x^2 translated 7 units down and 4 units to the left.

BladeRunner212

It is the graph of y = x² translated 7 units down and 4 units to the left.

Further explanation

There are four types of transformation geometry:

  • translation (or shifting),
  • reflection,
  • rotation, and
  • dilation (stretching or shrinking).  

In this case, the transformation is shifting vertically and horizontally.

  • Translation (or shifting): moving a graph on an analytic plane without changing its shape.  
  • Vertical shift: moving a graph upwards or downwards without changing its shape.  
  • Horizontal shift: moving a graph to the left or right downwards without changing its shape.  

Vertical Shift

Given the graph of y = f(x) and v > 0, we obtain the graph of:  

  • [tex]\boxed{ \ y = f(x) + v \ }[/tex] by shifting the graph of [tex]\boxed{ \ y = f(x) \ }[/tex] upward v units.
  • [tex]\boxed{ \ y = f(x) - v \ }[/tex] by shifting the graph of [tex]\boxed{ \ y = f(x) \ }[/tex] downward v units.  

Horizontal Shift

Given the graph of y = f(x) and h > 0, we obtain the graph of:  

  • [tex]\boxed{ \ y = f(x + h) \ }[/tex] by shifting the graph of [tex]\boxed{ \ y = f(x) \ }[/tex] to the left h units.  
  • [tex]\boxed{ \ y = f(x - h) \ }[/tex] by shifting the graph of [tex]\boxed{ \ y = f(x) \ }[/tex] to the right h units.

- - - - - - - - - -

Given:

[tex]\boxed{ \ y = x^2 \rightarrow \ ? \rightarrow  \ y = (x + 4)^2 - 7 \ }[/tex]

Clearly, to obtain the graph of [tex]\boxed{ \ y = (x + 4)^2 - 7 \ }[/tex] we must translate the graph of [tex]\boxed{ \ y = x^2 \ }[/tex].

  • [tex]\boxed{ \ y = x^2 \ }[/tex] translated 7 units down.
  • It becomes [tex]\boxed{ \ y = x^2 - 7 \ }[/tex]
  • Furthermore, [tex]\boxed{ \ y = x^2 - 7 \ }[/tex] translated 4 units to the left.

Thus, the result is [tex]\boxed{ \ y = (x + 4)^2 - 7 \ }[/tex]

Conclusion

The statement correctly describes the graph of y = (x + 4)² - 7 is the graph of y = x² translated 7 units down and 4 units to the left.

The answer is C.

Learn more  

  1. Transformations that change the graph of f(x) to the graph of g(x) https://brainly.com/question/2415963
  2. The similar problem https://brainly.com/question/1369568
  3. Which equation represents the new graph https://brainly.com/question/2527724

Keywords: each statement, describes, a transformation, the graph, y = x², which, correctly, y = (x + 4)² - 7, translation, shifting, left, down, upward, units, up,  horizontal, vertical

Ver imagen BladeRunner212

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