Hi,
When we express x^2 - 6x + 10 in the form (x + a)^2 + c,
we are completing the square of a quadratic expression.
In general, x^2 + px + q can be written as (x +
p/2)^2 + q - (p/2)^2, and this fact should be committed to
memory.
By completing the square of a quadratic equation
(i.e. y = x^2 + px + q), we will be able to find its minimum
y-value, which will be q - (p/2)^2. The x-coordinate of this
minimum turning point is x = -p/2.
For Q1,
x^2 - 6x + 10 = (x - 3)^2 + 10 - 9
= (x - 3)^2 + 1,
so that its minimum value is 1, and this occurs at x =
3.
Hope these help to clarify! Thanks!
Cheers,
Wen Shih
eh. my fren also taught me another way
is to expand the (x+a)^2
into x^2+ 2ax+a^2 +c or sth like tat
then we compare(x^2-6x+10) with that eqn
?