Chapter 3 Lesson 2 The Graph Translation Theorem

Vocabulary Translation Image – The result of a translation Preimage- The domain or set of domain values of a transformation, also known as the original graph Translation- A transformation that maps each point (x,y) to (x+h,y+k) where h and k are constants, and the point is moved vertically k units and horizontally h units

Translations Moving a point up or down (vertical translation) changes the y coordinate (4,6) moved up 5 units is (4,6+5) = (4,11) (3,1) vertical translation of 4 units is (3,1+4) = (3,5) (7,2) moved down 4 units is (7,2-4) = (7,-2) (2,3) vertical translation of -2 units is (2,3-2) = (2,1) Moving a point left or right (horizontal translation) changes the x coordinate (1,6) to the right 7 units is (1+7,6) =(8,6) (2,1) horizontal translation of 3 units is (2+3,1) = (5,1) (3,5) to the left 4 units is (3-4,5) = (-1,5) (4,2) horizontal translation of -1 units is (4-1,2) = (3,2)

Find Image of Each Point Under F if F(x,y)= (x+3,y-1) (2,-2) (3,1) (7,8) (p,q)

Writing Translation Rules Up 4 units and left 5 units F(x,y)= (x-5,y+4) Down 3 units and right 2 units F(x,y)=(x+2,y-3) Down 1 unit and left 2 units F(x,y)=(x-2,y-1) Up k units and right h units F(x,y)=(x+h,y+k)

Translating Different Equations Left or Right

Translating Different Equations Up or Down

Combining Translations

Equation for a Circle (x-h) 2 + (y-k) 2 = r 2 r= radius of circle Center of circle at (h,k) (x-2) 2 + (y+3) 2 = 9 Radius? Center? x 2 + (y-1) 2 = 2 Radius? Center? A circle has a radius of 2 and a center at (1,2), write an equation for the circle. A circle has a center at (5,0) and a radius of 6, write an equation for the circle.

Equation for a Parabola (x-h) 2 + k Vertex of parabola at (h,k) (x+1) 2 – 3 Vertex? (x-2) Vertex? A parabola has a vertex of (5,4), what would the equation be for the parabola? A parabola has a vertex of (-2,-1), what would the equation be for the parabola?

Homework Worksheet 3-2