Answer to Question #68585 in Algebra for Peter

Question

x² -10x + 33 ≡ (x - a)² + b

Work out the value of a and the value of b

What is the minimum value of x² - 10x + 33?

Answer 1

x^2-10x+33=x^2-10x+25+8=(x^2-10x+25)+8=(x-5)^2+8
a=5, b=8
The minimum value of the function will be obtained when the part of the equation that is squared is equal to zero (x=5):
(5-5)^2+8=8

Answer: a=5, b=8 , the minimum value is 8.