document.write( "Question 1179817: Find the domain and range of {(x,y)|y=3x^(2)-3x+4} \n" ); document.write( "
Algebra.Com's Answer #809410 by ikleyn(52794)\"\" \"About 
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document.write( "The given function  y = 3x^2 - 3x + 4 is a quadratic function.\r\n" );
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document.write( "The leading coefficient is positive, so the parabola plot is open upward.\r\n" );
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document.write( "The domain of the function is the set of all real numbers.      ANSWER\r\n" );
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document.write( "The range is the set of all real numbers from the minimum value (the vertex y-value) to infinity.\r\n" );
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document.write( "The minimum value of this quadratic function is at  x = \"-b%2F%282a%29\" = \"-%28-3%29%2F%282%2A3%29\" = \"1%2F2\".\r\n" );
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document.write( "The minimum y-value is  \"3%2A%281%2F2%29%5E2+-+3%2A%281%2F2%29%2B4\" = 3.25.\r\n" );
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document.write( "So the range of the function is  [3.25,oo).      ANSWER\r\n" );
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document.write( "            Plot of the function  y = \"3x%5E2+-+3x+%2B+4\"\r\n" );
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\n" ); document.write( "\n" ); document.write( "On finding the maximum/minimum of a quadratic function see the lessons\r
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\n" ); document.write( "\n" ); document.write( "    - HOW TO complete the square to find the minimum/maximum of a quadratic function\r
\n" ); document.write( "\n" ); document.write( "    - Briefly on finding the minimum/maximum of a quadratic function\r
\n" ); document.write( "\n" ); document.write( "    - HOW TO complete the square to find the vertex of a parabola\r
\n" ); document.write( "\n" ); document.write( "    - Briefly on finding the vertex of a parabola\r
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\n" ); document.write( "\n" ); document.write( "Consider these lessons as your textbook,  handbook,  tutorials and  (free of charge)  home teacher.\r
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\n" ); document.write( "\n" ); document.write( "Also,  you have this free of charge online textbook in ALGEBRA-I in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this textbook under the topic \"Finding minimum/maximum of quadratic functions\". \r
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\n" ); document.write( "\n" ); document.write( "Save the link to this online textbook together with its description\r
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\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-I
\n" ); document.write( "https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson\r
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\n" ); document.write( "\n" ); document.write( "to your archive and use it when it is needed.\r
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