Question 641414: Find the equation for a parabola that has zeros at - 6 and 4 and passes through the point (2,-48). What is the value of ' a ' ?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Find the equation for a parabola that has zeros at - 6 and 4 and passes
through the point (2,-48). What is the value of ' a ' ?
:
Using the form ax^2 + bx + c = y; write an equation for each point
x=-6; y=0
-6^2a - 6b + c = 0
36a - 6b + c = 0
:
x=4; y=0
16a + 4b + c = 0
:
x=2; y=-48
4a + 2b + c = -48
:
Adding all three equations eliminates b
36a - 6b + c = 0
16a + 4b + c = 0
4a + 2b + c = -48
--------------------
56a + 3c = -48
:
Eliminate b again with two equation
16a + 4b + c = 0
8a + 4b + 2c = -96; multiplied by 2
---------------------subtraction eliminates b
8a - c = 96
:
multiply by 3, pair with the other two unknown equation
56a + 3c = -48
24a - 3c = 288
-----------------adding eliminates c
80a = 240
a = 240/80
a = 3, which is the only coefficient they ask for
:
:
Find b and c to check this out
8(3) - c = 96
24 - c = 96
-c = 96-24
-c = 72
c = -72
:
Using the 3rd equation to find b
3(4) + 2b - 72 = -48
12 + 2b - 72 = -48
2b = -48 + 60
2b = 12
b = 6
:
The equation then: y = 3x^2 + 6x - 72, you can check all points
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