document.write( "Question 62265: graph Y=3x^2-8x+2 and give the vertex, domain and rage\r
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Algebra.Com's Answer #42992 by funmath(2933) $\"\"$ $\"About$

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graph Y=3x^2-8x+2 and give the vertex, domain and rage\r
\n" ); document.write( "\n" ); document.write( "This quadratic equation is in standard form: $\"y=ax%5E2%2Bbx%2Bc\"$
\n" ); document.write( "Your a=3, b=-8, c=2
\n" ); document.write( "We can find the x coordinate for the vertex with the formual $\"highlight%28x=-b%2F2a%29\"$
\n" ); document.write( " $\"x=-%28-8%29%2F%282%283%29%29\"$
\n" ); document.write( " $\"x=8%2F6\"$
\n" ); document.write( " $\"x=4%2F3\"$
\n" ); document.write( "Plug x=4/3 into your equation to find the y-coordinate of the vertex.
\n" ); document.write( " $\"y=3%284%2F3%29%5E2-8%284%2F3%29%2B2\"$
\n" ); document.write( " $\"y=3%2816%2F9%29-32%2F3%2B2\"$
\n" ); document.write( " $\"y=16%2F3-32%2F3%2B2\"$
\n" ); document.write( " $\"y=16%2F3-32%2F3%2B6%2F3\"$
\n" ); document.write( " $\"y=%2816-32%2B6%29%2F3\"$
\n" ); document.write( " $\"y=-10%2F3\"$
\n" ); document.write( "The vertex is (4/3,-10/3)
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\n" ); document.write( "The domain (possible x values) for all quadratic equations like this is ALL REAL NUMBERS. (x can be anything.) In set builder notation {x|x=R}, in interval notation (-infinity,infinity).
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\n" ); document.write( "The range (possible y values) is found by first looking at a. a=3--it is positive. That means that the parabola opens upward and the y coordinate of the vertex is it's lowest y. Therefore the range is {y|y>=-10/3}.
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\n" ); document.write( "Happy Calculating!!! \n" ); document.write( "

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