Question 2 The graph shows a translation of the parent function. Select the equation for the function g(x).

A)g(x)=(x+2)2+1
B)g(x)=(x+1)2−2
C)g(x)=(x−2)2−1
D)g(x)=(x−2)2+1

Option D: g(x) = (x - 2)² + 1

Step-by-step explanation:

The equation that represents the parent function of a parabola can be represented by f(x) = x², which is a quadratic (or square) function. It is one of the basic elementary functions commonly used in the field of Mathematics. Performing mathematical operations on a parent function that results into a new function represents the transformation of the parent graph.

This represents the vertical shift of the parent graph of a quadratic function.  

Horizontal translation:  y = (x + h )²

This represents the horizontal shift of the parent graph of a quadratic function.  

The given graph shows the translation of the parent function, where the vertex occurs at point, (2, 1). Since the graph is upward-facing, then it means that the vertex is its minimum point on the graph.

If we substitute the values of the vertex, (h, k) into the vertex form of a quadratic function, g(x) = a(x - h)² + k:

Vertex = (2, 1)

g(x) = a(x - 2)² + 1  

We can solve for the value of "a" by choosing another point from the graph, (1, 2). Substitute these coordinates into the vertex form:

g(x) = a(1 - 2)² + 1  

2 = a(1 - 2)² + 1  

2 = a(-1)² + 1  

2 = a(1) + 1

Subtract 1 from both sides to isolate "a":

2 - 1 = a(1) + 1 - 1

1 = a

Therefore, the quadratic function that represents the given graph is:

g(x) = (x - 2)² + 1, which matches Option D.

Additional Notes on the constant, "a":

The constant, "a" in the vertex form, g(x) = a(x - h)² + k  determines the  vertical stretch, compression, and reflection (across the x-axis) of the graph.

Keywords:

Parabola

Transformations of Quadratic Functions

Quadratic equations

Parent Function

Vertex form

Learn more about transformations of quadratic functions here:

answer;

the correct answer

just use google you beautiful person.

have a nice day < 3