Find an equation in the form y equals ax squared plus bx plus cy=ax2+bx+c for the parabola passing through the points. (11,negative 8−8), (negative 5−5,negative 164−164), (33,negative 36−36)
+130536 We have this system of equations
a(11)^2 + b(11) + c = -8 → 121a + 11b + c = -8 (1)
a(-5)^2 + b(-5) + c = -164 → 25a - 5b + c = -164 (2)
a(33)^2 + b(33) + c = -36 → 1089a + 33b + c = -36 (3)
Multiply (2) by -1 and add to (1) ......this gives
96a + 16b = 156 (4)
Multiply (1) by -1 and add to (3).......this gives
968a + 22b = -28 (5)
Multiply (4) by -22 and (5) by 16.....this gives
-2112a -352b = -3432 (6)
15488a +352b = - 448 (7)
Add (6) and (7) together
13376a = -3880 (8)
Divide both sides of (8) by 13376 and a = -485/1672
And using (4) to solve for b, we have
96(-485/1672) + 16b = 156 → b = 4803/418
And using (1) to solve for c, we have
121(-485/1672) + 11(4803/418) + c = -8 → c = -15093/152
So the equation is ... y = (-485/1672)x^2 + (4803/418)x - 15093/152
Here's the graph of the parabola......https://www.desmos.com/calculator/dukrb3wrm2
