Transformations of Quadratic Functions Instruction

(1) If the parabola of the form y = a(x - h)2 + k is always shifted horizontally h units and vertically k units, then its vertex is always (2) Enter the coordinates of the vertex of the graph of y = 2(x + 5)^2 − 4. Vertex: ?

1. (h, k) 2. (-5, -4)

(1) As |a| increases, the parabola becomes ___ (2) As |a| decreases, the parabola becomes ___

(1) narrower (2) wider

(1) Complete the square to write y = 3x^2 + 12x + 7 in vertex form, y = a(x - h)2 + k. y = 3(x^2 + 4x) + 7 y = 3(x^2 + 4x +4) + 7 - __(a)__ (2) When the above expression is written in vertex form, a is __(b)__, h is __(c)__, and k is __(d)__.

1. a = 12 2. b = 3 , h = -2 , k = -5

(1) Choose the equation that shows a step in the process of completing the square on the given quadratic. y = x^2 + 8x - 3 (2) The vertex form of the function is y= (x + __(a)__ )^2 + __(b)__

1. y = x^2 + 8x + 16 - 3 - 16 2. (a) = 4, (b) = -19

Select the graphs that have an equation with a < 0.

Second and Third Graph

Choose the graph of y = (x - 3)^2 + 1.

Third Graph

(1) Compare the graphs of the functions listed below. Function 1: y = 0.25x^2 Function 2: y = 4x^2 Function 3: y = -½x^2 Function 4: y = -16x^2 The graph of __(a)__ is the widest. The graph of __(b)__ is the narrowest. The graph of function 2 is __(c)__ the graph of function 3.

a. function 1 b. function 4 c. narrower than

(1) The graph of g(x) = (x + 2)^2 is a translation of the graph of f(x) __(a)__ by __(b)__ units. (2) The graph of h(x) = (x − 3)^2 is a translation of the graph of f(x) __(c)__ by __(d)__ units.

a. left b. 2 c. right d. 2

(1) The graph of g(x) = x2 + 2 is a translation of the graph of f(x) __(a)__ by __(b)__ units. (2) The graph of h(x) = x2 − 3 is a translation of the graph of f(x) __(c)__ by __(d)__ units.

a. up b. 2 c. down d. 3