2.5 Graphing Quadratic Functions

1. 2.5 Graphing Quadratic Functions

2. (aka parabola) There are two main methods for graphing a quadratic I. From Standard Form f (x) = ax2 + bx + c Axis of Symmetry: Vertex: y-int: (when x = 0) x-int: (when y = 0) set = 0 & solve (s1, 0) (s2, 0)

3. Ex 1) f (x) = 3x2 – 9x –12 a) Axis of Symmetry: b) Vertex: c) y-int: (0, ??) (0, –12)

4. 0 = 3x2 – 9x –12 • 0 = 3(x2 – 3x –4) • 0 = 3(x – 4)(x + 1) • x = 4, –1 Ex 1) f (x) = 3x2 – 9x –12 cont… d) x-int: (??, 0) e) Graph (4, 0) and (–1, 0) from prev: (0, –12)

5. push graph Ex 2) Finding zeros using calculator f (x) = 4x2 – 13x + 5 y = type in 4x2 – 13x + 5 2nd CALC 2: zero put cursor on left side & hit ENTER arrow over to right of it & hit ENTER ENTER again do same for other int 0.446 & 2.804

6. II. From Vertex Form Change standard to vertex form by completing the square and then use transformations of x2 to graph Ex 3) Graph f (x) = 2x2 + 12x + 17 f (x) = 2(x2 + 6x ) + 17 + 9 – 18 f (x) = 2(x + 3) 2 – 1 The graph of x2 has moved 3 left, 1 down and gotten skinnier by the number 2

7. y = ____(x – ____ ) 2 + ____ Ex 4) Do it the other way! Write equation from a picture vertex: (2 , 4) upside down  a is (–) skinny by 2  a = –2 How??? To find ‘a’: plug in a point (1, 2): y = a(x – 2)2 + 4 2 = a(1 – 2)2 + 4 –2 = a y = –2(x – 2) 2 + 4

8. Homework #205 Pg 91 #1–29 odd, 30–35 all, 36, 38, 46