4-2 Translating Parabolas notes

Integrated 24-2 Translating ParabolasSo, narrowest (largest a) to widest (smallest a):y x x22= 3 − 16 , y =− 5 x + 4x,y2= 0.8x+ 5 ,y = − −20.2 x 3Translations “slide”A translation changes only the position of a graph; it doesn’t change the size or shape of thegraph, or the direction that the graph opens.22Ex: The graph of y = 3( x −1) − 7 is a translation of the graph y = 3x.Translation of thegraph y = ax 2Equation of thetranslated graphh units right2y = a( x−h)h units left2y = a( x+h)k units up2y = ax + kk units down2y = ax − kSubtraction indicates a translation to the right.Addition indicates a translation to the left.Translations can also occur in two directions at the same time.*A graph can be translated to the right and up, to the right and down, to the leftand up, and to the left and down.Example 3Give the equation of the parabola that results when the graph ofdown and 3 units to the right.y4x2= is translated 5 unitsSolution2To translate the graph of y = 4x3 units to the right, replace x with (x-3).2y = 4( x − 3)22To translate the graph of y = 4( x − 3) down 5 units, subtract 5 from 4( x − 3) .2y = 4( x −3) − 52The equation of the parabola is y = 4( x −3) − 5Example 4Give the equation of the parabola that results when the graph ofto the left and 1 unit up.y4x2= is translated 7 unitsSolution:To translate the graph ofy = 4( x + 7 )To translate the graph ofy = + +24( x 7 ) 12yy2= 4x7 units to the left replace x with (x+7).2= 4( x + 7 ) up 1 unit, add 1 to24( x + 7 ) .