1.2 Parabola Stretches & Compressions Flashcards
Leading Coefficient
The constant multiplier for
the highest power term
y=ax²
a is the leading coefficient & x² the highest power term for parabolas
Hidden Coefficient
When the constant multiplier for a term is 1 it can be hidden
y=1x²=x²
a=1 is the hidden coefficient
Partially Hidden Coefficient
When the constant multiplier for a term is -1, only write the minus sign
y = -1x² = -x²
a= -1 is the partially hidden coefficient
Parabola will open Up
y=ax² OR y=a(x-h)²+k
a>0
a is positive
Parabola will open down
y=ax² OR y=a(x-h)²+k
a<0
a is negative
Parabola will be vertically stretched (tall & thin)
y=ax² OR y=a(x-h)²+k
a>1 or a<-1
a is greater than 1 or less than -1
Parabola will be vertically compressed (short & wide)
y=ax² OR y=a(x-h)²+k
-1<a<1
a is between -1 and 1, and often a fraction of 1
Up or down; stretched or compressed?
y=2x²
Opens up &
Stretched Vertically
a=2 which is positive and greater than 1
Up or down; stretched or compressed?
y=387.25x²
Opens up &
Stretched Vertically
a=387.25 which is positive and greater than 1
Up or down; stretched or compressed?
y=¼x²
Opens up &
Compressed Vertically
a=¼ which is positive and less than 1
Up or down; stretched or compressed?
y=0.342(x+2)² - 3
Opens up &
Compressed Vertically
a=0.342 which is positive and less than 1
Up or down; stretched or compressed?
y=-5x² - 2
Opens down &
Stretched Vertically
a= -5 which is negative and less than -1
Up or down; stretched or compressed?
y=-⅔x²
Opens down &
Compressed Vertically
a= -⅔ which is negative and between -1 and 1
Up or down; stretched or compressed?
y=-1.75x²
Opens down &
Stretched Vertically
a= -1.75 which is negative and less than -1
Up or down; stretched or compressed?
y=-(x+3)² + 1
Opens down &
No Vertical Stretch or Compression
a= -1 which is negative
