Question

Which response correctly writes the equation in vertex form for the function?

(1 point)
Responses

y=12(x+2)2−2
y equals Start Fraction 1 over 2 End Fraction left parenthesis x plus 2 right parenthesis squared minus 2

y=12(x−2)2
y equals Start Fraction 1 over 2 End Fraction left parenthesis x minus 2 right parenthesis squared

y=12(x+2)2
y equals Start Fraction 1 over 2 End Fraction left parenthesis x plus 2 right parenthesis squared

y=12(x+2)2+2

Answer 1

To convert a quadratic function into vertex form, the general form of vertex form is \( y = a(x - h)^2 + k \), where \((h, k)\) is the vertex of the parabola.

Based on the given responses, let's analyze each of them for correctness:

1. **Response 1**: \( y = \frac{1}{2}(x + 2)^2 - 2 \)
- This is in vertex form with vertex at \((-2, -2)\).

2. **Response 2**: \( y = \frac{1}{2}(x - 2)^2 \)
- This is in vertex form with vertex at \((2, 0)\).

3. **Response 3**: \( y = \frac{1}{2}(x + 2)^2 \)
- This is in vertex form with vertex at \((-2, 0)\).

4. **Response 4**: \( y = \frac{1}{2}(x + 2)^2 + 2 \)
- This is in vertex form with vertex at \((-2, 2)\).

Without the initial function being provided, we cannot definitively declare which response is correct. However, if we consider the format of vertex form to create an accurate response, any of these responses could be correct based on the vertex and the function's characteristics they are derived from.

Please check your original function and identify the vertex to select the correct response.