1.5 Quizizz Lesson

• ​Absolute Value symbol: |x| (two straight lines)

• |-4| = 4 (because -4 is 4 steps away from 0)

• Any negative input becomes positive, because distance has to be positive.

• When there is a negative in front of the absolute value sign we say we are taking the opposite of the absolute value.
   

• |5| --> The absolute value of 5.

  • |5| = 5

• -|5| --> The opposite of the absolute value of 5.

  • -|5| = -5

• |-5| --> The absolute value of negative 5.

  • |-5| = 5

• -|-5| --> The opposite of the absolute value of negative 5.

  • -|-5| = -5

• The absolute value of a number is the number of spaces from zero.

Graph the Absolute Value Function

How to type the absolute value sign on Desmos?

h-left or right

• a Compresses or stretches the graph vertically (Graph will Push TO and Pull AWAY from the X-axis)

• h Translates the graph of the absolute value function either to the left (+h) or right (-h) !

• k Translates the graph of the absolute value function either to the up (+k) or down (-k) !

• If "a" is positive the function opens up

• If "a" is negative, it is a reflection, meaning it opens down

• "a" is the slope of the branches of the graph

• The larger the "a" value, the more narrow it is

• "h" is a horizontal translation

• if |x - h| move the graph to the right "h" units

• if | x + h| move the graph to the left "h" units

• "k" is a vertical translation

• if "k" is positive it moves up

• if "k" is negative it moves down

• reflection

• vertical stretch by 2

• horizontal translation 7 units left

• vertical translation 3 units down

• either the highest or the lowest point on the graph

• has the coordinates (-h, k) the opposite of h and k
  

• h = -3

• k = 7

• vertex (-h, K)

• The vertex is located at (3, 7)