Posted by Ariel on Sunday, June 10, 2012 at 9:45pm.
Intersections with y=x^2 at x=-2 and x=4 describes two points:
(-2, y=(-2)^2) and (4, y=4^2)
Find the line between those two points.
For x = - 2
y = ( - 2 ) ^ 2 = 4
( x1 = - 2 , y1 = 4 )
For x = 4
y = 4 ^ 2 = 16
( x2 = 4 , y2 = 16 )
The line through two distinct points (x1, y1) and (x2, y2) is given by
y = y1 + [ ( y2 - y1 ) / ( x2 - x1 ) ] * ( x - x1 )
In your case :
x1 = - 2
y1 = 4
x2 = 4
y2 = 16
y = y1 + [ ( y2 - y1 ) / ( x2 - x1 ) ] * ( x - x1 )
y = 4 + [ ( 16 - 4 ) / ( 4 - ( - 2 ) ] * x - ( - 2 ) ]
y = 4 + [ 12 / ( 4 + 2 ) ] * ( x + 2 )
y = 4 + ( 12 / 6 ) * ( x + 2 )
y = 4 + 2 * ( x + 2 )
y = 4 + 2 x + 4
y = 2 x + 8
Proof :
For x = - 2
y = 2 * ( - 2 ) + 8 = - 4 + 8 = 4
( x1 = - 2 , y1 = 4 )
For x = 4
y = 2 * 4 + 8 = 8 + 8 = 16
( x2 = 4 , y2 = 16 )
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