We want to get y = a(x-h)²+k
y = x²-3x+6 in the form
Put brackets around the first two terms on the
right,
y = [x²-3x]+6
and since the coefficient of x² is 1 put 1
in front of the parentheses. Normally you
would factor out the coefficient of x²:
y = 1[x²-3x]+6
We complete the square inside the brackets:
1. Multiply the coefficient of x, which is -3
by
, getting
.
2. Square
getting
=
3. Add
, which is really 0, inside the
brackets:
y = 1[x²-3x+
-
]+6
Factor the first three terms inside the bracket like this
x²-3x+
= (x-
)(x-
) = (x-
)²
y = 1[(x-
)²-
]+6
Remove the bracket
y = 1(x-
)²-
+6
Write the 6 as
y = 1(x-
)²-
+
y = 1(x-
)²+
y = a(x-h)²+k
The vertex is (h,k) = (
,
)
Edwin