express the quadratic expression:
x^2 - 8x + 20
in the form:
(x-a)^2 +b
2006-10-22 12:11:07 · 4 answers · asked by amelia 2 in Education & Reference ➔ Homework Help
express the quadratic expression:
x^2 - 8x + 20 in the form (x-a)^2 +b
therefore deduce the least value of x^2 - 8x + 20
and deduce the value of x at which the least value of x^2 - 8x +30 occurs
2006-10-22 12:21:54 · update #1
Multiply out (x-a)^2 + b. You get x^2 - 2ax + a^2 + b.
Match this expression against x^2 - 8x + 20. Comparing like terms tells you that:
-8 = -2a
20 = a^2 + b.
Therefore, a=4, and b=4.
2006-10-22 12:19:52 · answer #1 · answered by James L 5 · 0⤊ 0⤋
You have to split the 20 = 16 + 4
Then complete the square:
x^2 - 8x + 16 + 4 = (x-4)^2 + 4
2006-10-22 19:16:12 · answer #2 · answered by linen 2 · 0⤊ 0⤋
(x-4)^2+4
2006-10-22 19:19:53 · answer #3 · answered by Anonymous · 0⤊ 0⤋
x² - 8x +20
is
x² -8x +16 +4
is
(x-4)²+4
[remember (x-a)² = x² -2xa +a²]
2006-10-22 19:15:59 · answer #4 · answered by Anonymous · 0⤊ 0⤋