Question 62069: Not in a text book.
The quadratic equation y=ax squared +bx +c=0 is used in signal processing to represent a more complex signal. This function passes through the points (in the form (x,y) (0,0) (2,5) and (6,10). Write down simultaneous equations in a, b and c and solve them to find the function. (Please show working out)
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! The quadratic equation y=ax squared +bx +c=0 is used in signal processing to represent a more complex signal. This function passes through the points (in the form (x,y) (0,0) (2,5) and (6,10). Write down simultaneous equations in a, b and c and solve them to find the function.
---------
Substitute each point into the quadratic form to get three equations:
c=0
a(4)+2b+c=5
a(36)+6b+c=10
-----------
Then:
1st: 4a+2b=5
2nd: 36a+6b=10
-------
Multiply 1st be 3 to get:
3rd: 12a + 6b=15
--------
Subtract 3rd from 2nd to get:
24a=-5
a=-5/24
----------
Substitute into 1st to solve for "b", as follows:
4(-5/24)+2b=5
-20/24+2b=120/24
2b=140/24
b=70/24
----------
EQUATION:
y=(-5/24)x^2+(70/24)x
y=(-1/24)(5x^2-70x)
---------
Cheers,
Stan H.
|
|
|
