Question 1163930
a parabola with the x intercepts at (-1, 0) and (3, 0) which passes through the point (1,-8)
------------------------------
y = ax^2 + bx + c is the parabola
---
At (-1,0):
0 = a*(-1)^2 -b + c
a - b + c = 0  ------ Eqn 1
========================
At (3,0):
0 = a*9 + 3b + c  
9a + 3b + c = 0   ---------- Eqn 2
========================
At (1,-8):
-8 = a + b + c
a + b + c = -8 ---- Eqn 3
a - b + c = 0  ------ Eqn 1
----------------------------- Subtract
2b = -8
b = -4
=========================
0 = a*9 + 3b + c  ---------- Eqn 2
9a + 3b + c = 0
9a + c = 12
 a + c = -4
-------------------------- Subtract
8a = 16
a = 2
=================
a - b + c = 0  ------ Eqn 1
2 + 4 + c = 0
c = -6
=======================
2x^2 - 4x - 6 = 0 is the parabola
---------------------------------------
Another method:
<pre>
| x   x^2   y   1|  
|-1    1    0   1|
| 3    9    0   1| = 0
| 1    1   -8   1|

</pre>
This method is easily made into an Excel sheet.