‘Find the constants a and b such that, for all values of x, x² + 6x + 20 = (x + a)² + b. Hence state the least values of x² + 6x + 20, and state also the value of x for which this least value occurs’.
I understand the start of the question: it is just completing the square.
X² + 6X +20 = (X + 3)² - 9 + 20 = (X + 3)² +11.
Therefore, a=3 and b=11.
However, I am unsure as to what the second part of the question (Hence state…) is actually asking me to do. If anybody could explain what it is asking, it would be appreciated.
I understand the start of the question: it is just completing the square.
X² + 6X +20 = (X + 3)² - 9 + 20 = (X + 3)² +11.
Therefore, a=3 and b=11.
However, I am unsure as to what the second part of the question (Hence state…) is actually asking me to do. If anybody could explain what it is asking, it would be appreciated.