SOLUTION: Find the domain and range of {(x,y)|y=3x^(2)-3x+4}

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Question 1179817: Find the domain and range of {(x,y)|y=3x^(2)-3x+4}
Answer by ikleyn(52787) About Me  (Show Source):
You can put this solution on YOUR website!
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The given function  y = 3x^2 - 3x + 4 is a quadratic function.


The leading coefficient is positive, so the parabola plot is open upward.


The domain of the function is the set of all real numbers.      ANSWER


The range is the set of all real numbers from the minimum value (the vertex y-value) to infinity.


The minimum value of this quadratic function is at  x = -b%2F%282a%29 = -%28-3%29%2F%282%2A3%29 = 1%2F2.


The minimum y-value is  3%2A%281%2F2%29%5E2+-+3%2A%281%2F2%29%2B4 = 3.25.


So the range of the function is  [3.25,oo).      ANSWER

Solved.     //     All questions are answered.


    



            Plot of the function  y = 3x%5E2+-+3x+%2B+4


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


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.