SOLUTION: Consider the general quadratic function f(x)= ax^2+bx+c, with a not equal to 0. a. Find the coordinated of the vertex in terms of a,b,and c. b. Find the conditions on a,b, and c

Question 1167495: Consider the general quadratic function f(x)= ax^2+bx+c, with a not equal to 0.
a. Find the coordinated of the vertex in terms of a,b,and c.
b. Find the conditions on a,b, and c that guarantee that the graph of f crosses the x-axis twice.
Answer by ikleyn(52835) (Show Source): You can put this solution on YOUR website!
.


(a)  x-coordinate of the vertex is equal to  x = .



(b)  The necessary and sufficient condition is   > 0.


     The discriminant of the equation must be positive real number.

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On finding the 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

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.

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