SOLUTION: a parabola with the x intercepts at (-1, 0) and (3, 0) which passes through the point (1, -8)

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Question 1163930: a parabola with the x intercepts at (-1, 0) and (3, 0) which passes through the point (1, -8)
Found 2 solutions by greenestamps, Alan3354:
Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


With x-intercepts at -1 and 3, the equation is of the form

y+=+a%28x-%28-1%29%29%28x-3%29

or

y+=+a%28x%2B1%29%28x-3%29

Plug in the coordinates of the given point (1,-8) to determine the value of the coefficient a:

-8+=+a%281%2B1%29%281-3%29

You can finish from there....

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
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:
| x   x^2   y   1|  
|-1    1    0   1|
| 3    9    0   1| = 0
| 1    1   -8   1|

This method is easily made into an Excel sheet.