The vertex form of the quadratic is y = (x - 6)² - 23.
What is the vertex form of f(x)?
For a quadratic equation with leading coefficient a and vertex (h, k), the vertex form is:
y = a*(x - h)² + k
The leading coefficient of:
f(x)= x² - 12x + 13
is 1.
The general quadratic:
y = ax² + bx + c
Has a vertex at x = -b/2a
For our equation we have:
x = -(-12)/2*1 = 6
Evaluating there we get:
f(6) = 6² - 12*6 + 13 = 36 - 72 + 13 = -23
So the vertex is at (6, -23), then the quadratic equation is:
y = (x - 6)² - 23