Question Complete the square to re-write the quadratic function in vertex form: \[ y=x^{2}-7 x+2 \] Answer Attemptiout of 2

1. Start with the quadratic function: \[ y = x^2 - 7x + 2 \] 2. Group the \( x \)-terms together: \[ y = \left(x^2 - 7x\right) + 2 \] 3. To complete the square, take the coefficient of \( x \), which is \(-7\). Half of \(-7\) is \(-\frac{7}{2}\). Square this value to get: \[ \left(-\frac{7}{2}\right)^2 = \frac{49}{4} \] 4. Add and subtract \(\frac{49}{4}\) inside the parentheses: \[ y = \left(x^2 - 7x + \frac{49}{4} - \frac{49}{4}\right) + 2 \] 5. Group the perfect square trinomial and combine the constant terms: \[ y = \left(x^2 - 7x + \frac{49}{4}\right) - \frac{49}{4} + 2 \] 6. The trinomial \(\left(x^2 - 7x + \frac{49}{4}\right)\) factors as: \[ \left(x - \frac{7}{2}\right)^2 \] So the function becomes: \[ y = \left(x - \frac{7}{2}\right)^2 - \frac{49}{4} + 2 \] 7. Express the \( 2 \) as \(\frac{8}{4}\) and simplify: \[ y = \left(x - \frac{7}{2}\right)^2 - \frac{49}{4} + \frac{8}{4} = \left(x - \frac{7}{2}\right)^2 - \frac{41}{4} \] 8. The vertex form of the quadratic function is: \[ y = \left(x - \frac{7}{2}\right)^2 - \frac{41}{4} \]