This preview shows page 1. Sign up to view the full content.
Unformatted text preview: =  2x − 3  by transforming the graph of the linear
function and then verify your graph by writing the absolute value function as
a piecewise function. o Draw the graph of y = 2x − 3 . Use a dashed line; part of this graph is not
used for the absolute value function’s graph. y
2 o The points on the xaxis and the points
above the xaxis are invariant points; they
will also be on the graph of the absolute
value function. Draw these points with a 2 0 2 x 2 solid line. o The points below the xaxis will be affected by the transformation; they will
be reflected about the xaxis to above the xaxis.
if 2x − 3 o  2x − 3  = 0
if
− (2 x − 3) if so y =  2x − 3  becomes y= Unit 6: Day 2 notes  Absolute Value Functions Page 3 of 4 GRAPHING y =  a(x − p)2 + q  , THE ABSOLUTE VALUE OF A QUADRATIC FUNCTION
example: Draw the graph of y =  x2 − 4x + 3  by transforming the graph of the
quadratic function and then verify your graph by writing the absolute value
function as a piecewise function.
o Draw the graph of
It's vertex equation is
The vertex is (2,−1) y = x2 − 4x + 3 y y = (x − 2)2 − 1 6 It's factored form is
y = (x − 1)(x − 3)
The xintercepts are (1,0) and (3,0) 4 2 Use a dashed line.
o The points on and above the xaxis are
invariant points. Draw these points with a
solid line. 0 2 x 4 o Reflect the points below the xaxis to above the xaxis. ( x − 2)2 − 1
if ( x − 1)( x − 3) > 0 o  x2 − 4x + 3  = 0
if ( x − 1)( x − 3) = 0
( x − 2)2 − 1 if ( x − 1)( x − 3) < 0
− ( x − 2)2 − 1 if x ≤ 1 or x ≥ 3 2
so y =  x − 4x + 3  becomes y = 2
− ( x − 2) + 1 if 1 < x < 3 exercise: Draw the graph of y =  x2 − 4  by
transforming the graph of the quadratic
function.
Then verify your graph by writing the
absolute value function as a piecewise
function. y
3 3 0 3 3 x Unit 6: Day 2 notes  Absolute Value Functions Page 4 of 4 exercise: Draw the graph of y =  x2 + 1  by
transforming the graph of the quadratic
function. y
3 3 0 x 3 3 2 [Answer: same as the graph of y = x + 1] exercise: Draw the graph of y =  −x2 − 1  by
transforming the graph of the quadratic
function. y
3 3 0 x 3 3 2 [Answer: same as the graph of y = x + 1] y EXTENSION
Graph y=  f (x)  2 if x > 2 for f (x) = x if − 2 ≤ x ≤ 2 −2 if x <...
View
Full
Document
This document was uploaded on 02/16/2014 for the course MATH PreCalcul at Holy Cross Regional High School.
 Fall '11
 Aytona
 Calculus, PreCalculus

Click to edit the document details