Complete the square to re-write the quadratic function in vertex form:
y=x 2+2x+8
To complete the square, we need to rearrange the quadratic function in the form of (x - h)^2 + k, where (h, k) gives the vertex of the parabola.
To rewrite y = x^2 + 2x + 8 in vertex form:
1. Take half of the coefficient of x and square it: (2/2)^2 = 1.
2. Add this value both inside and outside the parentheses on the right side of the equation:
y = x^2 + 2x + 1 + 8 - 1
= (x^2 + 2x + 1) + 7
3. Rearrange the terms:
y = (x+1)^2 + 7
Therefore, the quadratic function y = x^2 + 2x + 8 can be rewritten in vertex form as y = (x+1)^2 + 7.