document.write( "Question 629298: Find the quadratic polynomial whose graph goes through the points (−1,5), (0,5), and (2,29). \r
\n" ); document.write( "\n" ); document.write( "f(x)= _x2+_ x+_ <<< that form\r
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\n" ); document.write( "\n" ); document.write( "I got to the step 4a+2b+0=29\r
\n" ); document.write( "\n" ); document.write( "that was like my 6/7th step. I am getting stuck from there. Can i get any help please?
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Algebra.Com's Answer #396162 by Theo(13342)\"\" \"About 
You can put this solution on YOUR website!
it's a quadratic polynomial and it goes through the points:
\n" ); document.write( "(-1,5)
\n" ); document.write( "(0,5)
\n" ); document.write( "(2,29)
\n" ); document.write( "the general form of a quadratic equation is:
\n" ); document.write( "ax^2 + bx + c = 0
\n" ); document.write( "another form of the quadratic equation is:
\n" ); document.write( "y = ax^2 + bx + c
\n" ); document.write( "if it goes through the point (-1,5), then this equation becomes:
\n" ); document.write( "5 = a(-1)^2 + b(-1) + c
\n" ); document.write( "simplify this to get:
\n" ); document.write( "5 = a - b + c
\n" ); document.write( "if it goes through the point (0,5), then this equation becomes:
\n" ); document.write( "5 = c
\n" ); document.write( "if it goes through the point (2,29), then this equation becomes:
\n" ); document.write( "29 = a(2)^2 + b(2) + c
\n" ); document.write( "simplify this to get:
\n" ); document.write( "29 = 4a + 2b + c
\n" ); document.write( "we have 3 equations:
\n" ); document.write( "they are:
\n" ); document.write( "5 = a - b + c
\n" ); document.write( "5 = c
\n" ); document.write( "29 = 4a + 2b + c
\n" ); document.write( "since c = 5, we can substitute in the other 2 equations to get:
\n" ); document.write( "5 = a - b + 5
\n" ); document.write( "29 = 4a + 2b + 5
\n" ); document.write( "these simplify to:
\n" ); document.write( "a - b = 0
\n" ); document.write( "4a + 2b = 24
\n" ); document.write( "a - b = 0 results in a = b
\n" ); document.write( "substitute a for b in the other equation to get:
\n" ); document.write( "4a + 2a = 24
\n" ); document.write( "simplify to get:
\n" ); document.write( "6a = 24
\n" ); document.write( "a = 4
\n" ); document.write( "we now know that a = 4 and c = 5
\n" ); document.write( "we also know that b = which results in b = 4
\n" ); document.write( "we should have:
\n" ); document.write( "a = 4
\n" ); document.write( "b = 4
\n" ); document.write( "c = 5
\n" ); document.write( "let's see if that works.
\n" ); document.write( "our equation is:
\n" ); document.write( "y = 4x^2 + 4x + 5
\n" ); document.write( "when x is equal to -1, we get:
\n" ); document.write( "y = 4(-1)^2 + 4(-1) + 5 which simplifies to:
\n" ); document.write( "y = 4 - 4 + 5 which results in y = 5 which is correct because we are dealing with the point (-1,5)
\n" ); document.write( "our equation is:
\n" ); document.write( "y = 4x^2 + 4x + 5
\n" ); document.write( "when x = 0, our equation becomes:
\n" ); document.write( "y = 0 + 0 + 5 which results in y = 5 which is correct because we are dealing with the point (0,5)
\n" ); document.write( "when x = 2, our equations becomes:
\n" ); document.write( "y = 4(2)^2 + 4(2) + 5 which simplifies to:
\n" ); document.write( "y = 16 + 8 + 5 which simplifies further to:
\n" ); document.write( "y = 29 which is correct because we are dealing with the point (2,29)
\n" ); document.write( "looks like we're good and the equation i:
\n" ); document.write( "y = 4x^2 + 4x + 5\r
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