SOLUTION: Determine the values of a and b in the relation y = ax 2 + bx + 7 if the vertex is located at (4, -5)

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Question 1186905: Determine the values of a and b in the relation y = ax 2 + bx + 7 if the vertex is located at (4, -5)
Answer by ikleyn(52908) About Me  (Show Source):
You can put this solution on YOUR website!
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For any quadratic function  y = ax^2 + bx + c,  the x-coordinate of the vertex is


      x%5Bvertex%5D = -b%2F%282a%29.


THEREFORE, for your function  -b%2F%282a%29 = 4,  because 4 is the x-coordinate of the vertex (given).


It gives  -b = 4*(2a),  or  b = -8a,  which is your sough relation.    ANSWER

Solved and explained.

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On finding maximum/minimum of a quadratic function see the lessons

    - HOW TO complete the square to find the minimum/maximum of a quadratic function
    - Briefly on finding the minimum/maximum of a quadratic function
    - HOW TO complete the square to find the vertex of a parabola
    - Briefly on finding the vertex of a parabola


Consider these lessons as your textbook,  handbook,  tutorials and  (free of charge)  home teacher.
Learn the subject from there once and for all.


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 "Finding minimum/maximum of quadratic functions".


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.