Question

What are the transformations to this quadratic function y= (x+4) power of 2 - 8

Answer 1

Answer:

Horizontal shift of 4 units to the left.

Vertical translation of 8 units downward.  

Step-by-step explanation:

Given the quadratic function, y = (x + 4)² - 8, which represents the horizontal and vertical translations of the parent graph, y = x²:

The vertex form of the quadratic function is y = a(x - h)² + k

Where:

The vertex is (h , k), which is either the minimum (upward facing graph) or maximum (downward-facing graph).

The axis of symmetry occurs at x = h.

a =  determines whether the graph opens up or down, and makes the graph wider or narrower.

h = determines how far left or right the parent function is translated.

k = determines how far up or down the parent function is translated.

Going back to your quadratic function,

          y = (x + 4)² - 8

• The vertex occrs at (-4, -8)
• a is assumed to have a value of 1.
• Given the value of h = -4, then it means that the graph shifted horizontally by 4 units to the left.  
• Since k = -8, then it implies that the graph translated vertically at 8 units downward.

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