document.write( "Question 15590: How do you find the quadratic equation of a parabola with a vertex of (8, 102), a y-intercept of (0, 98.6) and a zero of (16,0)? I have tried to solve the equation -(b/2a) =8, but that hasn't worked out well. I've also tried to solve for a or b since I know that c is equal to 98.6, but so far I cannot get the right equation. All I have is that 64a + 8b + 98.6 = 102 and 256a + 16b + 98.6 = 0. I know a is a negative number, but that is the only other information I have. \n" ); document.write( "
Algebra.Com's Answer #7749 by khwang(438)\"\" \"About 
You can put this solution on YOUR website!
(8, 102), a y-intercept of (0, 98.6) and a zero of (16,0)? I have tried to solve the equation -(b/2a) =8, but that hasn't worked out well. I've also tried to solve for a or b since I know that c is equal to 98.6, but so far I cannot get the right equation. All I have is that 64a + 8b + 98.6 = 102 and 256a + 16b + 98.6 = 0.\r
\n" ); document.write( "\n" ); document.write( " I think that you started from \"y+=+ax%5E2+%2B+bx+%2B+c+\"
\n" ); document.write( " that is a long way for this question.\r
\n" ); document.write( "\n" ); document.write( " Try to start up with \"y+-+102+=+a%28x++-+8%29%5E2+\"
\n" ); document.write( " (same meaning as -b/2a =8 but easier)\r
\n" ); document.write( "\n" ); document.write( " and use point (16,0) to get -102 = 64 a
\n" ); document.write( " then we have a = - 51/32 and the equation of the parabola.
\n" ); document.write( "
\n" ); document.write( " to get check if (0,98.6) [a very uugly number] is on the curve or not.
\n" ); document.write( " If not the question is wrong. (I guess so) and so no solution.\r
\n" ); document.write( "\n" ); document.write( " What happened ???
\n" ); document.write( " Because (8,102) cannot be the vertex, the question with wrong given
\n" ); document.write( " condition.\r
\n" ); document.write( "\n" ); document.write( " Normally, if we know the vertex then one more point is enough to
\n" ); document.write( " determine the parabolic function.\r
\n" ); document.write( "\n" ); document.write( " So, unfortunately, I guess you have to solve
\n" ); document.write( " this two ugly equations:\r
\n" ); document.write( "\n" ); document.write( " 64a + 8b + 98.6 = 102 ...(1)
\n" ); document.write( " 256a + 16b + 98.6 = 0....(2)\r
\n" ); document.write( "\n" ); document.write( " By (2)-(1)*2: ..... a = ??? then b =???
\n" ); document.write( " to find a & b.\r
\n" ); document.write( "\n" ); document.write( " And the final solution means (8,102) is just a point on the parabola
\n" ); document.write( " but not the vertex.
\n" ); document.write( "
\n" ); document.write( " Good luck!\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " Kenny
\n" ); document.write( " PS: I think you can understand what I mean.
\n" ); document.write( " Normally, I don't answer such kinds of simple questions.
\n" ); document.write( " Since, you showed your work, I am gald to guide you some short cut.\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );