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