Question

Given that x^2 - 5x + 13 = (x - p)^2 + q for all values of x, calculate the value of p and q.
Hence, state

(a) the minimum value of x^2 - 5x + 13
(b) the value of x at which the minimum value occurs.
Sketch the curve y = x^2 - 5x + 13.

Need some help with this. Thx! (:

Answer 1

\[\left(x-\frac{5}{2}\right)^2+\frac{27}{4} \]
Minimum at (5/2, 27/4)
x=5/2

Answer 2

Thanks again! (: