SOLUTION: Determine the equation of the parabola where the points (-5, -8) and (1, -20) lie on the parabola and the parabola has an axis of symmetry of x=-3

Algebra ->  Rational-functions -> SOLUTION: Determine the equation of the parabola where the points (-5, -8) and (1, -20) lie on the parabola and the parabola has an axis of symmetry of x=-3      Log On


   

Question 1010470: Determine the equation of the parabola where the points (-5, -8) and (1, -20) lie on the parabola and the parabola has an axis of symmetry of x=-3
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The general form is:
+y+=+a%2Ax%5E2+%2B+b%2Ax+%2B+c+
-----------------
Plug the given points into the general equation
( -5, -8 )
+-8+=+a%2A%28-5%29%5E2+%2B+b%2A%28-5%29+%2B+c+
(1) +-8+=+25a+-+5b+%2B+c+
-------------------
( 1, -20 )
+-20+=+a%2A1%5E2+%2B+b%2A1+%2B+c+
(2) +-20+=+a+%2B+b+%2B+c+
---------------------
The formula for the x-coordinate of the vertex is:
+x%5Bv%5D+=+-b%2F%282a%29+
+-3+=+-b%2F2a+
(3) +b+=+6a+
-----------------
Subtract (2) from (1)
(1) +-8+=+25a+-+5b+%2B+c+
(2) +20+=+-a+-+b+-+c+
-----------------------
+12+=+24a+-+6b+
Plug (3) into this result
+12+=+24a+-+6%2A%28+6a+%29+
+12+=+24a+-+36a+
+12+=+-12a+
+a+=+-1+
and
(3) +b+=+6a+
(3) +b+=+6%2A%28-1%29+
(3) +b+=+-6+
and
(2) +-20+=+a+%2B+b+%2B+c+
(2) +-20+=+-1+-+6+%2B+c+
(2) +c+=+-20+%2B+7+
(2) +c+=+-13+
------------------------
+y+=+a%2Ax%5E2+%2B+b%2Ax+%2B+c+
+y+=+-x%5E2++-6x+-+13+
---------------------
check:
(-5,-8)
+y+=+-x%5E2++-6x+-+13+
+-8+=+-%28-5%29%5E2++-6%2A%28-5%29+-+13+
+-8+=+-25+%2B+30+-+13+
+-38+=+-25+-+13+
+-38+=+-38+
OK
---------------
You can check ( 1, -20 )
Here's the plot:
+graph%28+400%2C+400%2C+-10%2C+2%2C+-20%2C+1%2C+-x%5E2+-+6x+-+13+%29+