Answer:
Horizontal translation of the parent graph
Step-by-step explanation:
<h2><u>Definitions</u>:</h2>
In the <u>vertex form</u> of a quadratic function, f(x) = a(x - h)² + k, where:
- (h, k) = vertex of the graph
- <em>a</em> = determines the width and direction of the graph's opening.
A <u>horizonal translation</u> to the parent graph is given by, y = f(x - h), where:
- <em>h</em> > 0 ⇒ Horizontal translation of <em>h</em> units to the right
- <em>h</em> < 0 ⇒ Horizontal translation of |<em>h </em>| units to the left
In the graph of g(x) = (x + 12)², the <u>vertex</u> occurs at point (-12, 0).
While the <u>vertex</u> of the parent graph, f(x) = x² occurs at point, (0, 0).
<h2><u>Answers</u>:</h2>
Since the vertex of g(x) occurs at point, (-12, 0), substituting the value of (<em>h</em>, <em>k </em>) into the vertex form will result into:
g(x) = a(x - h)² + k
g(x) = [x - (-12)]² + 0
g(x) = (x + 12)² + 0
g(x) = (x + 12)²
Therefore, the graph of g(x) = (x + 12)² represents the horizontal translation of the parent graph, f(x) = x², where the graph of g(x) is <em>horizontally</em> translated 12 units to the left.
