completing square (a maths )

用戶209290

2009-01-15 2:08 am

completing square 點計 ? can you show me 5 example have steps for amaths quadratic equations only (not for maths )

can you give me some question for me to exercise ( no link ) plz post it !!

urgent .

回答 (1)

用戶10012

2009-01-17 9:45 pm

✔ 最佳答案

Sample 1. y = x^2 + 8x + 1.
Step 1: Think of a value of k such that x^2 + 8x + k is a perfect square. So k is 16, which equals to x^2 + 8x + 16 = (x + 4)^2.
Step 2: Adjust the content of y such that it contains (x+ 4)^2. So
y = x^2 + 8x + 16 - 15 = (x+ 4)^2 - 15.
Sample 2. y= 2x^2 + 5x + 4.
Step 1: Factor out the coefficient of the x^2 term. So y = 2(x^2 + 5x/2) + 4.
Step 2: Repeat step 1 in sample 1, we get x^2 + 5x/2 = (x + 5/4)^2 - 25/16.
so y = 2[(x+ 5/4)^2 - 25/16] + 4.
= 2(x + 5/4)^2 - 25/8 + 4
= 2(x + 5/4)^2 + 7/8.

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