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

Algebra ->  Rational-functions -> 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      Log On


   

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(52832) About Me  (Show Source):
You can put this solution on YOUR website!
.

(a)  x-coordinate of the vertex is equal to  x = -b%2F%282a%29.



(b)  The necessary and sufficient condition is  b%5E2+-+4ac > 0.


     The discriminant of the equation must be positive real number.

------------------

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.