Express x^2-5x+8 in the form (x-a) ^2+b

x^2 - 5x + 8 = (x - 5/2) ^2 + 7/4

Step-by-step explanation:

(x - a) ^2 + b = x^2 - 2ax + a^2 + b

equate to your quadratic:

x^2 - 5x + 8 = x^2 - 2ax + (a^2 + b)

equating coefficients (ignoring x^2 as the coefficient is 1 for both)

for x:

-5 = - 2a - -> a = 5/2

for x^ (0) : 8 = a^2 + b, note a = 5/2

thus,

8 = (5/2) ^2 + b

8 = 25/4 + b

b = 8 - 25/4 = 32/4 - 25/4 = (32 - 25) / 4 = 7/4

hence a = 5/2, b = 7/4

thus,

x^2 - 5x + 8 = (x - 5/2) ^2 + 7/4