Question

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.

Answer 1

• Vertex Form: $y=(x-h)^2+k$ , 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.

Answer 2

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:  

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

Horizontal Shift

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

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

- - - - - - - - - -

Given:

$\boxed{ \ y = x^2 \rightarrow \ ? \rightarrow \ y = (x + 4)^2 - 7 \ }$

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

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

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

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) brainly.com/question/2415963
2. The similar problem brainly.com/question/1369568
3. Which equation represents the new graph 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