Question 1179817
.
<pre>

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.      <U>ANSWER</U>


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/(2a)}}} = {{{-(-3)/(2*3)}}} = {{{1/2}}}.


The minimum y-value is  {{{3*(1/2)^2 - 3*(1/2)+4}}} = 3.25.


So the range of the function is  [3.25,oo).      <U>ANSWER</U>
</pre>

Solved.  &nbsp;&nbsp;&nbsp;&nbsp;//  &nbsp;&nbsp;&nbsp;&nbsp;All questions are answered.



<pre>
    {{{graph( 400, 400, -5, 5, -5, 15,        
              3x^2 - 3x + 4
)}}}



            Plot of the function  y = {{{3x^2 - 3x + 4}}}
</pre>


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


&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/HOW-TO-complete-the-square-of-a-quadratic-function-to-find-its-minimum-maximum.lesson>HOW TO complete the square to find the minimum/maximum of a quadratic function</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/Briefly-on-How-to-complete-the-square-of-a-quadratic-function-to-find-its-minimum-maximum.lesson>Briefly on finding the minimum/maximum of a quadratic function</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/HOW-TO-complete-the-square-to-find-the-vertex-of-a-quadratic-function.lesson>HOW TO complete the square to find the vertex of a parabola</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/Briefly-on-finding-the-vertex-of-a-parabola.lesson>Briefly on finding the vertex of a parabola</A>



Consider these lessons as your textbook, &nbsp;handbook, &nbsp;tutorials and &nbsp;(free of charge) &nbsp;home teacher.

Learn the subject from there once and for all.



Also, &nbsp;you have this free of charge online textbook in ALGEBRA-I in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A>.


The referred lessons are the part of this textbook under the topic "<U>Finding minimum/maximum of quadratic functions</U>". 



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.