1 / 14

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

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 = 5 x 2 y = 4 x 2 + 1 y = - 2 x 2 – 6 x + 3. Vertex is (0,1). Axis of symmetry is x = 0. Vertex is (-1.5,7.5). Axis of symmetry is x = -1.5. 4.2.

jael
Download Presentation

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

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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.

  2. 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

  3. 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.

  4. 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)

  5. 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)

  6. 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.

  7. 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).

  8. 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.

  9. 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

  10. 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

  11. 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

  12. 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

  13. 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)

More Related