Need help solving this ### Completing the Square for Quadratic Functions#### Question 8:Complete the square on the function \( g(x) = x^2 - 4x + 1 \) so it is written in vertex form. Explain what transformations have happened to the parent quadratic function whose vertex is at \((0,0)\).#### Solution Explanation:1. **Starting Function:** \[ g(x) = x^2 - 4x + 1 \]2. **Rewrite with Completing the Square:** - Take the coefficient of \( x \), divide it by 2, and then square it: \( (-4/2)^2 = 4 \). - Add and subtract this square within the function to create a perfect square trinomial: \[ g(x) = x^2 - 4x + 4 - 4 + 1 = (x - 2)^2 - 3 \]3. **Vertex Form:** \[ g(x) = (x - 2)^2 - 3 \]#### Transformations:- **Horizontal Shift:** By rewriting the function as \( (x - 2) \), the graph of \( g(x) \) shifts 2 units to the right.- **Vertical Shift:** With the \(- 3\) outside the squared term, the graph shifts 3 units downward.Hence, the combined transformations from the parent function \((x^2)\) to the transformed function \((x - 2)^2 - 3\) are:- Rightward shift by 2 units.- Downward shift by 3 units.#### Summary:The final vertex of the quadratic function \( g(x) \) is \( (2, -3) \). The parent function \( f(x) = x^2 \), initially at vertex \((0,0)\), undergoes transformations to arrive at the new vertex position at \((2, -3)\).

Name: Need help solving this ### Completing the Square for Quadratic Functio
Uploaded: 2024-03-20T07:06:27.000Z
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Description: Need help solving this ### Completing the Square for Quadratic Functions#### Question 8:Complete the square on the function \( g(x) = x^2 - 4x + 1 \) so it is written in vertex form. Explain what transformations have happened to the parent quadratic