To rewrite the quadratic function f(x) = x² + 6x + 4 in vertex form, we need to complete the square.
1. Start with the given function:
f(x) = x² + 6x + 4
2. Focus on the quadratic and linear terms, x² + 6x. To complete the square, take half of the coefficient of x (which is 6), square it, and add and subtract this value:
Half of 6 is 3, and 3² is 9. So, we rewrite the equation introducing and removing 9:
f(x) = (x² + 6x + 9) – 9 + 4
3. Now simplify:
f(x) = (x + 3)² – 5
This expression is now in vertex form, which is f(x) = a(x – h)² + k. Here, (h,k) is the vertex of the parabola.
4. Therefore, the vertex form of the function is:
f(x) = (x + 3)² – 5
The vertex of the parabola represented by this function is at the point (-3, -5).