<PRE><B>Question 1120312</B>
Find a quadratic model for the set of values. 
x -2, 0, 4 
f(x) 4, 6, -38 
:
 x | y
-------
-2 | 4
 0 | 6
 4 |-38
:
Use the form ax^2 + bx + c = y
When x=0, y=6, therefore c = 6
:
when x=-2; y=4
(-2^2)a + - 2b + 6 = 4
4a - 2b = 4 - 6
4a - 2b = -2
:
when x=4; y=-38
16a + 4b + 6 = -38
16a + 4b = -38 - 6
16a + 4b = -44
simplify, divide by 2
8a + 2b = -22
:
4a - 2b = -2
8a + 2b = -22
---------------addition eliminates b, find a
12a + 0 = -24
a = -24/12
a = -2
:
Find b
4(-2) - 2b = -2
-8 - 2b = -2
-2b = -2 + 8
-2b = 6
b = 6/-2
b = -3
:
The equation f(x) = -2x^2 - 3x + 6, is the quadratic model
{{{ graph( 300, 200, -6, 5, -40, 20, -2x^2 - 3x + 6, -38) }}}
green line = -38
</PRE>