Question

How does the graph of g(x) = (x+12)^{2}" align="absmiddle" class="latex-formula"> relate to the graph of f(x) = $x^{2}$

Answer 1

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.