Transformations Review Vertex form: y = a(x – h) 2 + k The vertex form of a quadratic equation allows you to immediately identify the vertex of a parabola. The vertex is the ordered pair (h, k). Also, x = h is the axis of symmetry and k is the maximum or minimum (optimal) y-value.

Vertical Stretch & Compress: Vertex form: y = a(x – h) 2 + k This tells us which way the parabola opens If a is positive, then the parabola opens up If a is negative, then the parabola opens down If a > 1 or a < -1, then the graph gets “skinny” or “vertically stretched” It is vertically stretched by a factor of “a” If a (If –1< a <1, the graph gets “wider” or “vertically compressed” by a factor of “a”)

Let’s graph and label them now x y y = x 2 y = 2x 2 y = -2x 2

Vertical Shift Up or Down: Vertex form: y = a(x – h) 2 + k This moves the parabola up or down (it is the y-coordinate of the vertex) If K is positive, the parabola moves up If K is negative, the parabola moves down

Let’s graph and label them now x y y = x 2 y = x y = x 2 - 1

Horizontal Shift Right or Left: Vertex form: y = a(x – h) 2 + k This indicates whether the parabola shifts left or right (it is the x- coordinate of the vertex). If subtracting a positive h, then the parabola shifts right If subtracting a negative h, the parabola shifts left. Example: (x – 2) 2  the parabola shift right 2 units (x – -2) 2 becomes  (x + 2) 2  the parabola shift left 2 units

Let’s graph and label them now x y y = x 2 y = (x+2) 2 y =(x–2) 2

Order of Transformations: Transformations from the parabola y = x 2 to y = a(x – h) 2 + k are done in this order 1.Translation left or right  h 2.Vertical stretch or compression  a 3.Reflection about the x-axis  a 4.Translation up or down  k