1. 3.2 (M2) Warm Up  Find the vertex, axis of symmetry, t-chart, graph, domain, range and min/max value. 1. y = 2x² - 5x + 3 2. y = 5x² + 1

2. 3.1 (M2) Daily Assessment  Find the vertex, axis of symmetry, t- chart, graph, domain, range and min/max value.  Show work! 1. y = ½ x² - 2x - 2 2. y = x² + 2

3. 3.2 (M2) Graphing Quadratic Functions in Vertex or Intercept Form

4. Vertex and Intercept Form  Vertex Form: y =a(x-h) 2 + k (h,k) is the vertex Notice-you take the opposite of h for the vertex  Intercept Form: y = a(x-p)(x-q) x intercepts are (p,0) and (q,0) Axis of symmetry is between 2 points X= p + q 2

5. GUIDED PRACTICE for Examples 1 and 2 Graph the function. Label the vertex and axis of symmetry. 1. y = (x + 2) 2 – 3 2. y = –(x + 1) 2 + 5 X=-2 (-2,-3) (-1,5) X=-1

6. GUIDED PRACTICE for Examples 3 and 4 Graph the function. Label the vertex, axis of symmetry, and x -intercepts. 5. y = (x – 3)(x – 7)6. f (x) = 2(x – 4)(x + 1) (3, 0)(7, 0) X=5 (5,-4) (-1, 0) X= 1.5 (4, 0) (1.5, -12.5)

7. GUIDED PRACTICE for Examples 3 and 4 7. y = –(x + 1)(x – 5) X Intercepts: Domain: Range: Vertex: Axis of Symmetry:

8. EXAMPLE 5 Change from intercept form to standard form Write y = –2(x + 5)(x – 8) in standard form. y = –2(x + 5)(x – 8) Write original function. = –2(x 2 – 8x + 5x – 40) Multiply using FOIL. = –2(x 2 – 3x – 40) Combine like terms. = –2x 2 + 6x + 80 Distributive property

9. EXAMPLE 6 Change from vertex form to standard form Write f (x) = 4(x – 1) 2 + 9 in standard form. f (x) = 4(x – 1) 2 + 9 Write original function. = 4(x – 1) (x – 1) + 9 = 4(x 2 – x – x + 1) + 9 Multiply using FOIL. Rewrite (x – 1) 2. = 4(x 2 – 2x + 1) + 9 Combine like terms. = 4x 2 – 8x + 4 + 9 Distributive property = 4x 2 – 8x + 13 Combine like terms.