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Coolmath Precalculus Review Calculus Preview
Lesson 9 - Graphing - Sideways Parabolas (page 3 of 6)
---- This Precalculus review (Calculus preview) lesson explains how to graph sideways parabolas.

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SHIFTS:

Standard Parabola Guy:

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

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

* shifts towards positive x's

Standard Parabola Guy shifted right to x = 3

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

* shifts towards negative x's

Standard Parabola Guy shifted left to x = -2

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 an up-n-down shift!

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

* shifts 1 towards positive y's!

Sideways Parabola Guy shifted up 1 to y = 1

x = ( y + 2 )^2 ... the + 2 tells you to shift to y = -2 ... ( -2 + 2 )^2 = ( 0 )^2

* shifts 2 towards negative y's!

Sideways Parabola Guy shifted down 2 to y = -2

Continued on the next page

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