SOLUTION: For my homework problem, I知 given a quadratic equation to turn into the formula to find h and k, the vertex. Can I have a step by step explanation how I can get from the quadratic

Algebra ->  Sequences-and-series -> SOLUTION: For my homework problem, I知 given a quadratic equation to turn into the formula to find h and k, the vertex. Can I have a step by step explanation how I can get from the quadratic      Log On


   

Question 1104413: For my homework problem, I知 given a quadratic equation to turn into the formula to find h and k, the vertex. Can I have a step by step explanation how I can get from the quadratic to vertex?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
As an alternative, you CAN try to work backward from the 'vertex' form into the polynomial form.

Assuming "a" is 1, then y=%28x-h%29%5E2%2Bk, for vertex being (h,k).

y=x%5E2-2hx%2Bh%5E2%2Bk, by doing the multiplication and simplification.

This corresponds to y=x%5E2%2Bbx%2Bc.
You have b=-2h and c=h%5E2%2Bk.
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These should also help you:
LESSON: Meaning of Completing The Square
https://www.algebra.com/my/Completing-the-Square-Using-Pictures.lesson?content_action=show_dev

LESSON: How to Complete The Square and Solve Quadratic Equation
https://www.algebra.com/my/Completing-the-Square-to-Solve-General-Quadratic-Equation.lesson?content_action=show_dev

Answer by ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!
.
Transformation from general quadratic form to vertex form is called "completing the square".

See the lessons
    - HOW TO complete the square - Learning by examples
    - HOW TO solve quadratic equation by completing the square - Learning by examples
in this site.


Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this textbook under the topic "Quadratic equations".


Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.