The graph of a transformed function is shown. Determine the parent function and the equation of the transformed function. vertex: (-2,0)

Question

(1 point)
Responses

The parent function is y=(x−2)2
. The equation of the transformed function is y=x2
.
The parent f unction is y is equal to open paren x minus 2 close paren squared. The equation of the transformed function is y is equal to x squared.

The parent function is y=x2
. The equation of the transformed function is y=(x−2)2
.
The parent function is y is equal to x squared. The equation of the transformed function is y is equal to open paren x minus 2 close paren squared.

The parent function is y=x2
. The equation of the transformed function is y=(x+2)2
.
The parent function is y is equal to x squared. The equation of the transformed function is y is equal to open paren x plus 2 close paren squared.

The parent function is y=(x+2)2
. The equation of the transformed function is y=x2
.

Answer 1

To analyze the information provided, let's start by identifying the parent function and the transformed function.

The vertex of a quadratic function is given in the form:

\[ y = a(x-h)^2 + k \]

where \((h, k)\) is the vertex of the parabola. Here, the vertex is given as \((-2, 0)\), which means \(h = -2\) and \(k = 0\).

The parent function (without any transformations) is:

\[ y = x^2 \]

Now, incorporating the vertex into the vertex form of a quadratic function, we have:

\[ y = a(x - (-2))^2 + 0 \implies y = a(x + 2)^2 \]

Since there is no additional information to indicate a stretching or compressing factor (the value of \(a\) is not specified), we can assume \(a = 1\) for the basic transformation, leading us to:

\[ y = (x + 2)^2 \]

So, the final answers are:

• The parent function is \(y = x^2\).
• The equation of the transformed function is \(y = (x + 2)^2\).

Now let's match this to your options:

The correct response from your options is:

"The parent function is y = x^2. The equation of the transformed function is y = (x + 2)^2."