Quadratic relations
Tpes Of Transformations
horizontal translation
Determined by the "h" value in the y=a(x-5)^2 +k formula
The value of "h" can shift the parabola horizontally right or left
if h>0 then it is translated to the right
if h<0 then it is translated the the left
vertical translation
Determined by the "k" value in the y=a(x-5)^2+k formula
The value of "k" can shift the parabola vertically up or down
if k>0 then it is translated up
if k<0 then it is translated down
vertical compression
A parabola is vertically compressed when the "a" value is more than -1 but less than 1
-1<a<1
vertical stretch
A parabola is vertically stretched when the value of "a" is more than 1 but less than -1
1<a<-1
reflection
A parabola is reflected when the value of "a" is less than 0
a<0
y=a(x-h)^2 +k
A
if the value of "a" is positive the parabola opens upward
a=1
if the value of "a" is negative the parabola opens downward
a=-1
H
K
The vertex of a parabola are the "h" and
"k" values
(h,k)
the point (x,y) where the parabola changes direction
The axis of symmetry is the "k" value
ex. if the equation was y=-2(x-1)^2 the axis of symmetry would be 1
Vertical line drawn through the vertex
Zeros
the x intercepts, set y as 0
ex.
y intercept
set x as 0
ex.
Min/Max Value
if the parabola opens upward it has a min value
if the parabola opens downward it has a max value
y=ax^2
Vertex Form
base quadratic
Linear and Non-Linear
Linear relations
first differences are equal
a straight line
Non-linear relations
points do no lie along a line (curved)
second differences are equal