document.write( "Question 828362: Hi,
\n" ); document.write( "So I missed my Pre-Ap Algebra II class, and I was wondering how I would be able to find a quadratic function that includes each set of Values.
\n" ); document.write( "So, the question that I was working on gave me three points, which are (1,-2),(2,-2), and (3,-4).
\n" ); document.write( "I did look in the textbook, and I attempted to try each. This is what I have so far.
\n" ); document.write( "*y=ax^2+bx=c
\n" ); document.write( "-2=A(-1)^2+b(1)+c
\n" ); document.write( "-2=a+b+c
\n" ); document.write( "*y=ax^2+bx=c
\n" ); document.write( "-2=a(2)^2+b(2)+c
\n" ); document.write( "-2=4a+2b+c
\n" ); document.write( "*y=ax^2+bx=c
\n" ); document.write( "-4=a(3)^2=b(3)=c
\n" ); document.write( "-4=9a+3b+c
\n" ); document.write( "So thats what I have so far, but in the example i noticed it said \"use one of the methods in chap.3\" and solve. Im not sure what to do after all of that from above. I just want to know which way is the easiest and will help me with my following homework problems. I was also wondering if there was any way to check it to make sure my answer will be right with this and the upcoming problems that I have to solve.
\n" ); document.write( "Thank you so much for your time and help \n" ); document.write( "
Algebra.Com's Answer #499338 by MathTherapy(10552)\"\" \"About 
You can put this solution on YOUR website!
Hi,
\n" ); document.write( "So I missed my Pre-Ap Algebra II class, and I was wondering how I would be able to find a quadratic function that includes each set of Values.
\n" ); document.write( "So, the question that I was working on gave me three points, which are (1,-2),(2,-2), and (3,-4).
\n" ); document.write( "I did look in the textbook, and I attempted to try each. This is what I have so far.
\n" ); document.write( "*y=ax^2+bx=c
\n" ); document.write( "-2=A(-1)^2+b(1)+c
\n" ); document.write( "-2=a+b+c
\n" ); document.write( "*y=ax^2+bx=c
\n" ); document.write( "-2=a(2)^2+b(2)+c
\n" ); document.write( "-2=4a+2b+c
\n" ); document.write( "*y=ax^2+bx=c
\n" ); document.write( "-4=a(3)^2=b(3)=c
\n" ); document.write( "-4=9a+3b+c
\n" ); document.write( "So thats what I have so far, but in the example i noticed it said \"use one of the methods in chap.3\" and solve. Im not sure what to do after all of that from above. I just want to know which way is the easiest and will help me with my following homework problems. I was also wondering if there was any way to check it to make sure my answer will be right with this and the upcoming problems that I have to solve.
\n" ); document.write( "Thank you so much for your time and help
\n" ); document.write( "

\n" );
document.write( "Your 3 equations in 3 unknowns are correct, up to this point. 
\n" );
document.write( " 
\n" );
document.write( "You can use ELIMINATION (see below) to solve for the variables, and determine the quadratic equation.
\n" );
document.write( "You can also use MATRICES to solve for the variables, if you're familiar with this method.\r
\n" );
document.write( "\n" );
document.write( " a +  b + c = - 2 -------- eq (i)
\n" );
document.write( "4a + 2b + c = - 2 -------- eq (ii)
\n" );
document.write( "9a + 3b + c = - 4 -------- eq (iii) \r
\n" );
document.write( "\n" );
document.write( "- 3a – b = 0 ------- Subtracting eq (ii) from eq (i) ------ eq (iv) 
\n" );
document.write( "- 5a - b = 2 ------- Subtracting eq (iii) from eq (ii) ------ eq (v)
\n" );
document.write( "      2a = - 2 ----- Subtracting eq (v) from eq (iv)
\n" );
document.write( "       a = \"%28-+2%29%2F2\", or \"highlight%28a+=+-+1%29\" 
\n" );
document.write( "- 3(- 1) – b = 0 ------- Substituting 1 for a in eq (iv) 
\n" );
document.write( "       3 – b = 0 
\n" );
document.write( "         - b = - 3
\n" );
document.write( "           b = \"%28-+3%29%2F-+1\", or \"highlight%28b+=+3%29\"
\n" );
document.write( " 1 + (3) + c = - 2 ------- Substituting 1 for a, and – 3 for b in eq (i)
\n" );
document.write( "   1 + 3 + c = - 2 
\n" );
document.write( "       4 + c = - 2
\n" );
document.write( "           c = - 2 - 2, or \"highlight%28c+=+-+4%29\"
\n" );
document.write( "With a being - 1, b being 3, and c being - 4, the equation: \"y+=+ax%5E2+%2B+bx+%2B+c+\" becomes:
\n" );
document.write( "\"y+=+-+1%28x%5E2%29+%2B+3%28x%29+%2B+-+4\"
\n" );
document.write( "Quadratic equation thus formed: \"highlight_green%28y+=+-+x%5E2+%2B+3x+-+4%29\"\r
\n" );
document.write( "\n" );
document.write( "To check if this is the correct equation, just substitute each coordinate point into the equation, and each 
\n" );
document.write( "equation should prove true.\r
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document.write( "\n" );
document.write( "You can do the check!! \r
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document.write( "\n" );
document.write( "Send comments, “thank-yous,” and inquiries to “D” at MathMadEzy@aol.com.
\n" );
document.write( "Further help is available, online or in-person, for a fee, obviously. 
\n" );
document.write( "	
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document.write( "For FREE info and answers to questions about the ASVAB exam, the NYS 3 – 8 city/state wide exams, 
\n" );
document.write( "GENERAL MATH QUESTIONS, MATH HOMEWORK QUESTIONS, or MATH QUESTIONS related to the Regents Integrated Algebra,
\n" );
document.write( "Regents Geometry, Regents Algebra 2/Trigonometry, SHSAT, COOP/HSPT/TACHS, PSAT, SAT, ACT, SSAT/ISEE, GRE, CLEP,
\n" );
document.write( "and the GED, you can visit: http://asvabstudyzone.freeforums.net/. \n" );
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