d the turning point of \( y=x^{2}+4 x-3 \) by completing the square

To find the turning point of the quadratic function \( y = x^2 + 4x - 3 \) by completing the square, we will follow these steps: 1. **Identify the quadratic and linear coefficients**: The quadratic term is \( x^2 \) and the linear term is \( 4x \). 2. **Complete the square**: - Start with the expression \( x^2 + 4x \). - To complete the square, take half of the coefficient of \( x \) (which is \( 4 \)), square it, and add and subtract that value inside the equation. - Half of \( 4 \) is \( 2 \), and squaring it gives \( 4 \). 3. **Rewrite the expression**: \[ y = (x^2 + 4x + 4) - 4 - 3 \] \[ y = (x + 2)^2 - 7 \] 4. **Identify the turning point**: - The vertex form of a quadratic function is \( y = a(x - h)^2 + k \), where \( (h, k) \) is the vertex (turning point). - From our completed square form \( y = (x + 2)^2 - 7 \), we can see that: - \( h = -2 \) - \( k = -7 \) Thus, the turning point of the function \( y = x^2 + 4x - 3 \) is at the point \( (-2, -7) \).