Graphing Form. ( h, k ): The Key Point The value of a Positive: Same OrientationIf it Increases:...
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Transcript of Graphing Form. ( h, k ): The Key Point The value of a Positive: Same OrientationIf it Increases:...
Graphing Form
Graphing Form( h, k ): The Key Point
The value of aPositive: Same Orientation If it Increases: Vertical Stretch
Negative: Flipped If it Decreases: Vertical Compression
Parent Graph: When a=1, h=0, and k=0
Quadratic Cubic
Hyperbola Square Root
Exponential
3y a x h k
1x hy a k y a x h k
x hy ab k
2y a x h k
Example: Quadratic
New Equation:
23 4y x
y = 4
x = 3
Transformation: Shift the parent graph three units to the right and four units up.
(3,4)
Example: Cubic
3 5y x
y = 5
x = 0
Transformation: Flip the parent graph and shift it five units up.
New Equation:
Transformation:
(0,5)
Example: Hyperbola
14 3xy y = -3
x = -4
Transformation: Shift the parent graph four units to the left and three units down.
New Equation:
Transformation:
(-4,-3)
Example: Square Root
6y x y = 0
x = -6
Transformation: Shift the parent graph six units to the left.
New Equation:
Transformation:
(-6,0)
Example: Exponential
53 2 2
xy
y = 2
x = 5
a = 3
Transformation: Shift the parent graph five units to the right and two units up. Then stretch the
graph by a factor of 3.
New Equation:
Transformation:
(5,2)
Linear Function
y xParent Equation
Graphing Form
y a x h k
Unless specified, you do not need to have the answer in y=mx+b form!
Point: Slope:(h,k) a
Example: Linear
y a x h k
y = 4
x = -6
Slope = ½
Transformation: A line with slope ½ that passes through the point (-6,4).
12 6 4y x New Equation:
Slope Point
(-6,4)
Absolute Value Function
y xParent Equation
Graphing Form
y a x h k
Absolute value can be found
in the calculator:
a) MATH
b) Right to NUM
c) 1. abs(
Example: Absolute Value
y = 4
x = -3
Transformation: Flip the parent graph and shift it three units to the left and four units up.
Transformation:
3 4y x New Equation:(-3,4)
Equation for a Circle
2 2 25x y Example
Graphing Form
2 2 2x h y k r
Center: Radius:(0,0)
Center: Radius:(h,k)
25 5
2r r
Example: Circle
y = -1
x = 4
Transformation: A circle centered at (4,-1) whose radius is 4.
Transformation:
2 24 1 16x y
New Equation:
Center:
Radius:
(4,-1)
16 4NO!Is a circle a function?
(4,-1)
Logarithmic Function
logby xParent Equation
Graphing Form
logby a x h k
Example: Exponential
log 3 2y x y = 2
x = 3
Transformation: Shift the parent graph three units to the right and two units up.
New Equation:
Transformation: