To rewrite the quadratic function f(x) = x² – 12x + 26 in vertex form, we first need to complete the square.
1. Start with the original equation:
f(x) = x² – 12x + 26
2. Focus on the x² – 12x part. To complete the square, take the coefficient of x (which is -12), divide it by 2 to get -6, and then square it to get 36.
3. Rewrite the equation by adding and subtracting this value (36) inside the function:
f(x) = (x² – 12x + 36) – 36 + 26
4. This simplifies to:
f(x) = (x – 6)² – 10
5. Now we can express it in vertex form:
f(x) = (x – 6)² – 10
In this vertex form, it’s clear that the vertex of the parabola is at the point (6, -10).