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

Graph Quadratic Functions in Vertex or Intercept Form 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

Vertex Form (h, k) (h, k) 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 a parabola with vertex (h, k). (h, k) y = x2 (h, k) 2. The axis of symmetry is x = h x = h Axis of symmetry 3. The graph opens up if a > 0 and opens down if a < 0.

Opens down a < 0. (-1 < 0) 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)

GUIDED PRACTICE 12 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)

Intercept Form y = a (x – p) (x – q) 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 p and 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.

Graph the function. 6. y = (x – 3) (x – 7) 7. f (x) = 2(x – 4) (x + 1) 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).

x - intercepts occur at the points (– 1, 0) and (5, 0). 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.

Changing quadratic functions from intercept form or vertex form 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: F O I L (x + 4)(x + 7) = x2 + 7x + 4x + 28 = x2 + 11x + 28

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) = – 2 (x2 – 8x + 5x – 40) = – 2 (x2 – 3x – 40) = – 2x2 + 6x + 80

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 = 4(x – 1) (x – 1) + 9 = 4(x2 – x – x + 1) + 9 = 4(x2 – 2x + 1) + 9 = 4x2 – 8x + 4 + 9 = 4x2 – 8x + 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

Homework: p. 249: 3-52 (EOP) GUIDED PRACTICE 9. 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)