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Sideways Parabolas

INSIDE     ( )^2SHIFTS:

Standard Parabola Guy:

(I'm just going to draw quick rough sketches.)

y = ( x - 3 )^2 ... shift right to x = 3

y = ( x + 2 )^2 ... shift left to x = -2


*Shifts towards positive x's


*Shifts towards negative x's


graph of y = ( x - 3 )^2 ... standard parabola guy shifted 3 to the right (towards positive x's)


graph of y = ( x + 2 )^2 ... standard parabola guy shifted 2 to the left (towards negative x's)

y = ( x - h )^2
These are locked together...

x is a back-n-forth guy, so the
h is the back-n-forth shift!

Sideways Parabola Guy:

x = ( y - k )^2
These are locked together...

y is an up-n-down guy, so the
k is the up-n-down shift!

(Again, I'm just going to do quick sketches -- you should make yours the official way and label 3 points.)

x = ( y - 1 )^2 ... shifts to y = 1 ... ( 1 - 1 )^2 = ( 0 )^2

x = ( y + 2 )^2 ... shifts to y = -2 ... ( -2 + 2 )^2 = ( 0 )^2


*Shifts 1 towards positive y's!


*Shifts 2 towards negative y's!


x = ( y - 1 )^2 ... sideways parabola shifted up 1 (towards positive y's)


graph of x = ( y + 2 )^2 ... sideways parabola shifted down 2 (towards negative y's)

YOUR TURN:

Graph

x = - ( y - 3 )^2

x = 2 ( y + 1 )^2