"a" Value
What happens if "a" is negative?
The graph of the parabola opens down.
What is unique about the "h" value?
It is always the opposite sign of what is shown in the equation.
What is the A.O.S.?
It is the Axis of Symmetry, a dashed vertical line that divides the parabola in half so that it is symmetric on the left and right sides.
y = -( x + 6 )2 -9
Does it open up or down? Why?
Down, "a" value is -1.
y = x2
Find the vertex.
( 0 , 0 )
What happens if "a" is positive?
The graph of the parabola opens up.
y= (x - 4)2 + 5
What is (h , k)?
(4 , 5)
If the vertex is (3 , 7), what is the A.O.S.?
x = 3
y = 2( x - 3 )2 + 7
What is the vertex?
( 3 ,7 )
y = -4( x + 1 )2 - 3
What is the vertex?
( -1 , -3 )
If "a" = 1/2 the transformation of the graph in relationship to the parent function is what?
Vertical Shrink
y = ( x + 2 )2 - 6
What is ( h , k )?
( -2 , -6 )
If the vertex is ( -5, 6 ), what is the A.O.S.?
x = -5
y = -( x + 2 )2 +7
Does the graph of this quadratic create a max or min?
Max
y = -3 ( x + 5 )2
What is the A.O.S.?
x = -5
If a=-5 the transformation of the graph in relationship to the parent function is a
Vertical Stretch
Reflection (Opens Down)
The graph translates 3 units to the right and 5 units down from the parent function.
What is (h , k)?
( 3 , -5 )
y = ( x - 4 )2- 8
What is the A.O.S.?
x = 4
y = ( x - 1)2 + 3
Describe the translations.
It translates 1 unit right and 3 units up.
y = 4( x + 1 )2 - 4
What is the y intercept?
( 0 , 0 )
If 0< |a| < 1 , what type of dilation is it?
Vertical Shrink
y = -2x2 + 6
What is (h , k)?
( 0 , 6 )
True or False?
y = -6x2 -7
The A.O.S. is x = -7.
False
y = -2( x + 3 )2 - 4
Describe the transformations in relationship to the parent function.
Translates 3 to the right and 4 down.
Vertical stretch by a factor of 2.
Reflects across the x axis
When writing a transformation, if it is stated "it reflects across the x-axis", what must be true?
a is negative.