document.write( "Question 66247This question is from textbook
\n" ); document.write( ": Please help me solve this equation. \"Find a, b, and c so that the parabola whose equation is y=ax^2+bx+c has its vertex (3,2) and passes through the point (-1,10)\". I have tried plugging in the point, but I cannot seem to figure it out. Thank you. \n" ); document.write( "
Algebra.Com's Answer #46996 by ankor@dixie-net.com(22740)\"\" \"About 
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Please help me solve this equation. \"Find a, b, and c so that the parabola whose equation is y=ax^2+bx+c has its vertex (3,2) and passes through the point (-1,10)\". I have tried plugging in the point, but I cannot seem to figure it out.
\n" ); document.write( ":
\n" ); document.write( "Two coordinates are given: the vertex x=3,y=2 and x=-1,y=10
\n" ); document.write( ":
\n" ); document.write( "Using x=3,y=2, the 1st equation
\n" ); document.write( "a(3^2) + 3b + c = 2
\n" ); document.write( "9a + 3b + c = 2
\n" ); document.write( ":
\n" ); document.write( "Using x=-1,y=10, find the 2nd equation
\n" ); document.write( "a(-1^2) - 1b + c = 10
\n" ); document.write( "a - b + c = 10
\n" ); document.write( ":
\n" ); document.write( "They gave x=3,y=2 as the vertex so the axis of symmetry would be x=3 and from that we can derive a 3rd coordinate.
\n" ); document.write( "The point x=-1 is 4 units to the left of +3 so if we go 4 units to the right of
\n" ); document.write( " +3 we have a point x=7,y=10.
\n" ); document.write( "The 3rd equation would be a(7^2) + 7b + c = 10; which is: 49a + 7b + c = 10
\n" ); document.write( ":
\n" ); document.write( "We have 3 equations and 3 unknowns a,b,c
\n" ); document.write( "Subtract the 1st eq from the 3rd eq, eliminate c:
\n" ); document.write( "49a + 7b + c = 10
\n" ); document.write( " 9a + 3b + c = 2
\n" ); document.write( "--------------------subtract
\n" ); document.write( "40a + 4b = 8
\n" ); document.write( ":
\n" ); document.write( "Subtract the 2nd equation from the 1st equation, eliminate c again:
\n" ); document.write( "9a + 3b + c = 2
\n" ); document.write( " a - b + c = 10
\n" ); document.write( "-----------------Subtract
\n" ); document.write( "8a + 4b = -8
\n" ); document.write( ":
\n" ); document.write( "Subtract the resulting equation and eliminate b
\n" ); document.write( "40a + 4b = 8
\n" ); document.write( " 8a + 4b = -8
\n" ); document.write( "--------------Subtract
\n" ); document.write( "32a = +16
\n" ); document.write( "a = 16/32
\n" ); document.write( "a = .5
\n" ); document.write( ":
\n" ); document.write( "Use eq, 8a + 4b = -8, substitute .5 for a to find b:
\n" ); document.write( "8(.5) + 4b = -8
\n" ); document.write( "4 + 4b = -8
\n" ); document.write( "4b = -12
\n" ); document.write( "b = -12/4
\n" ); document.write( "b = -3
\n" ); document.write( ":
\n" ); document.write( "Substitute in the 2nd equation to find c:
\n" ); document.write( ".5 - (-3) + c = 10
\n" ); document.write( "3.5 + c = 10
\n" ); document.write( "c = 10-3.5
\n" ); document.write( "c = +6.5
\n" ); document.write( ":
\n" ); document.write( "our equation is: y = .5x^2 - 3x + 6.5
\n" ); document.write( "It would look like this:
\n" ); document.write( "\"+graph%28+300%2C+200%2C+-4%2C+10%2C+-5%2C+15%2C+.5x%5E2+-+3x+%2B+6.5%29+\"
\n" ); document.write( ":
\n" ); document.write( "Note that it passes thru coordinates -1,10 and vertex is 3,2
\n" ); document.write( ":
\n" ); document.write( "Could you follow this OK?\r
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