Graph each function. Label the vertex and axis of symmetry.

1. 4.2 WARM-UP Graph each function. Label the vertex and axis of symmetry. Vertex is (0,0). Axis of symmetry is x = 0. y = 5x2 y = 4x2 + 1 y = -2x2 – 6x + 3 Vertex is (0,1). Axis of symmetry is x = 0. Vertex is (-1.5,7.5). Axis of symmetry is x = -1.5.

3. 4.2 Graph Quadratic Functions in Vertex or Intercept Form In the previous lesson we graphed quadratic functions in Standard Form:y = ax2 + bx + c, a ≠ 0 Today we will learn how to graph quadratic functions in two more forms: Vertex Form Intercept Form

4. Vertex Form Graph Vertex Form: y = a (x– h)2+k And Here Is The Final Text Box For this this is just a text box to cover part of the text!!!; Dfsasfal;dkj Characteristics of the graph of: y = a (x– h)2+k y = a (x– h)2+k This is another text box to take up room! 1. The graph is aparabolawith vertex (h,k). (h, k) y = x2 (h, k) 2. The axis of symmetry isx = h x = h Axis of symmetry 3. The graph opens up if a > 0 and opens down if a< 0.

5. GUIDED PRACTICE Graph the function. Label the vertex and axis of symmetry. 2. y = (x + 2)2– 3 Vertex (h, k) = (– 2, – 3). Axis of symmetry is x = – 2. 3. y = –(x + 1)2+ 5 Vertex (h, k) = (– 1, 5). Axis of symmetry is x = – 1. Opens down a < 0. (-1 < 0)

6. 12 GUIDED PRACTICE 4. f (x) = (x –3)2– 4 Vertex (h, k) = ( 3, – 4). Axis of symmetry is x = 3. Opens up a > 0. (1/2 < 0)

7. Intercept Form Graph Intercept Form: y = a (x – p) (x – q) Here Comes One Last Line To Cover All The graph Characteristics of the graph of y = a (x – p) (x – q): x = (p + q) / 2 1.The x – intercepts are pand q, so the points (p, 0) and (q, 0) are on the graph. y=a (x – p) (x – q) 2. The axis of symmetry is halfway between (p, 0) and (q, 0) and has equation: x = (p + q) / 2 (q, 0) (p, 0) 3. The graph opens up if a > 0 and opens down if a< 0.

8. Graph the function. 6. y = (x – 3) (x – 7) x - intercepts occur at the points (3, 0) and (7, 0). Axis of symmetry is x = 5 Vertex is (5, – 4). 7. f (x) = 2(x – 4) (x + 1) x - intercepts occur at the points (4, 0) and (– 1, 0). Axis of symmetry is x = 3/2. Vertex is (3/2, 25/2).

9. GUIDED PRACTICE 8. y = – (x + 1) (x – 5) x - intercepts occur at the points (– 1, 0) and (5, 0). Vertex is (2, 9). Axis of symmetry is x = 2.

10. Changing quadratic functions from interceptform or vertexform to standard form. FOIL Method: To multiply two expressions that each contain two terms, add the products of the First terms, the Outer terms, the Inner terms, and the Last terms. Example: FOIL (x + 4)(x + 7) = x2 + 7x + 4x + 28 = x2 + 11x + 28

11. EXAMPLE 5 Change frominterceptform tostandard form. Write y = – 2 (x + 5) (x – 8) in standard form. y = – 2 (x + 5) (x – 8) = – 2 (x2 – 8x + 5x – 40) = – 2 (x2 – 3x – 40) = – 2x2 + 6x + 80

12. EXAMPLE 6 Change fromvertexform tostandard form. Write f (x) = 4 (x – 1)2 + 9 in standard form. f (x) = 4(x – 1)2 + 9 = 4(x – 1) (x – 1) + 9 = 4(x2 – x – x + 1) + 9 = 4(x2 – 2x + 1) + 9 = 4x2 – 8x + 4 + 9 = 4x2 – 8x + 13

13. GUIDED PRACTICE Write the quadratic function in standard form. 7. y = – (x – 2) (x – 7) y = – (x – 2) (x – 7) = – (x2 – 7x – 2x + 14) = – (x2 – 9x + 14) = – x2 + 9x – 14 8. f(x)= – 4(x – 1) (x + 3) = – 4(x2 + 3x – x – 3) = – 4(x2 + 2x – 3) = – 4x2 – 8x + 12

14. GUIDED PRACTICE 9. y = – 3(x + 5)2 –1 y = – 3(x + 5)2 –1 = – 3(x + 5) (x + 5) –1 = – 3(x2 + 5x + 5x + 25) –1 = – 3(x2 + 10x + 25) –1 = – 3x2 – 30x – 75 – 1 = – 3x2 – 30x – 76 Homework: p. 249: 3-52 (EOP)