precalculus/trigonometry
posted by Ariel on .
Find a formula for the given linear function.
The graph of h intersects the graph of y = x^2 at x = 2 and x = 4

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 )