document.write( "Question 537951: What is the graph of this functions?
\n" ); document.write( "y= 1/2x^2 -3x+11/2\r
\n" ); document.write( "\n" ); document.write( "y= -2x^2+4x+3 \n" ); document.write( "
Algebra.Com's Answer #353120 by lwsshak3(11628)\"\" \"About 
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What is the graph of this functions?
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\n" ); document.write( "Problem 1.
\n" ); document.write( "y= 1/2x^2 -3x+11/2
\n" ); document.write( "complete the square
\n" ); document.write( "y=(1/2)(x^2-6x+9)+11/2-9/2
\n" ); document.write( "y=(1/2)(x-3)^2+1
\n" ); document.write( "This is an equation of a parabola of standard form: y=A(x-h)^2+k, with (h,k) being the (x,y) coordinates of the vertex. Parabola opens upwards.
\n" ); document.write( "For given equation:
\n" ); document.write( "vertex: (3,1)
\n" ); document.write( "A=1/2
\n" ); document.write( "x-intercepts
\n" ); document.write( "set y=0
\n" ); document.write( "(1/2)(x-3)^2+1=0
\n" ); document.write( "(x-3)^2=-2
\n" ); document.write( "x-intercepts: none
\n" ); document.write( "..
\n" ); document.write( "y-intercept
\n" ); document.write( "set x=0
\n" ); document.write( "y=1/2x^2 -3x+11/2
\n" ); document.write( "y=11/2
\n" ); document.write( "Because the parabola is symmetrical about its axis of symmetry(x=3), this gives another point (6,11/2)
\n" ); document.write( "..
\n" ); document.write( "With coordinates of the vertex, the y-intercept, point (6,11/2), no x-intercepts and the knowledge the parabola opens upwards, you should easily be able to graph given function
\n" ); document.write( "..
\n" ); document.write( "Problem 2.
\n" ); document.write( "y= -2x^2+4x+3
\n" ); document.write( "complete the square
\n" ); document.write( "y=-2(x^2-2x+1)+3+2
\n" ); document.write( "y=-2(x-1)^2+5
\n" ); document.write( "This is an equation of a parabola of standard form: y=-A(x-h)^2+k, with (h,k) being the (x,y) coordinates of the vertex. Parabola opens downwards.
\n" ); document.write( "For given equation:
\n" ); document.write( "vertex: (1,5)
\n" ); document.write( "A=-2
\n" ); document.write( "x-intercepts
\n" ); document.write( "set y=0
\n" ); document.write( "-2(x-1)^2+5=0
\n" ); document.write( "-2(x-1)^2=-5
\n" ); document.write( "(x-1)^2=5/2
\n" ); document.write( "take sqrt of both sides
\n" ); document.write( "x-1=±√(5/2)≈±1.58
\n" ); document.write( "x=1±1.58
\n" ); document.write( "x=2.58 and -0.58
\n" ); document.write( "..
\n" ); document.write( "y-intercept
\n" ); document.write( "set x=0
\n" ); document.write( "y=-2x^2+4x+3=3
\n" ); document.write( "Because the parabola is symmetrical about its axis of symmetry(x=1), this gives another point (2,3)
\n" ); document.write( "..
\n" ); document.write( "With coordinates of the vertex, the y-intercept, point (2,3), x-intercepts, and the knowledge the parabola opens downwards, you should easily be able to graph given function.
\n" ); document.write( "..
\n" ); document.write( "See the following graphs as visual checks on the answers:
\n" ); document.write( "Because the parabola is symmetrical about its axis of symmetry(x=3), this gives another point (6,11/2)
\n" ); document.write( "With coordinates of the vertex, the y-intercept, point (6,11/2) and the knowledge the parabola opens upwards, you should easily be able to graph given function. See graph below as a visual check on the answers. Red curve for problem 1 and green curve for problem 2
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