SOLUTION: convert y=x^2+6x-10 to vertex form completing the square. convert y=x^2-9x+3 to vertex form completing the square.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: convert y=x^2+6x-10 to vertex form completing the square. convert y=x^2-9x+3 to vertex form completing the square.      Log On


   



Question 252702: convert y=x^2+6x-10 to vertex form completing the square.
convert y=x^2-9x+3 to vertex form completing the square.

Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
Let's start with the first equation and then repeat process for second:
(i) +y+=+x%5E2+%2B+6x+-+10
STEP #1: re write the equation as
(ii) X%5E2+%2B+6X+%2B+___+=+10+%2B+___+
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STEP #2: take 1/2 middle term number and square it. put that answer in the blanks. We get
(iii) X%5E2+%2B+6X+%2B+3%5E2+=+10+%2B+3%5E2
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STEP #3: write the left side as a quantity squared and equalling the right.
(iv) %28X+%2B+3%29%5E2+=+19
This is vertex form.
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(v) y = x^2 - 9x + 3
STEP #1: re write the equation as
(ii) X%5E2+-+9X+%2B+___+=+3+%2B+___+
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STEP #2: take 1/2 middle term number and square it. put that answer in the blanks. Sometimes it's easier to say [middle number/2]. Don't forget your signs. We get
(iii) X%5E2+-+9X+%2B+%28-9%2F2%29%5E2+=+3+%2B+%28-9%2F2%29%5E2
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STEP #3: write the left side as a quantity squared and equalling the right.
(iv) %28X+-+9%2F2%29%5E2+=+%2893%2F4%29
This is vertex form.