Y= a ( x - h )2 + k Algebra 2: Notes 4.1 & 4.2: Pg.236 Pg.245 Pg.246

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Y= a ( x - h )2 + k Algebra 2: Notes 4.1 & 4.2: Pg.236 Pg.245 Pg.246 Graph Quadratic Functions in Standard, Vertex, or Intercept Form. GOALS: “” Pg.236 Pg.245 Pg.246 Quadratic Function: Minimum Value: Parabola: Pg.238 Vertex: Maximum Value: Axis of Symmetry: Vertex Form: Intercept Form: The Forms: Vertex Form Y= a ( x - h )2 + k Example 1: Can we multiply? If so give dimensions of the answer. a>0 opens up a<0 opens down |a|>1 narrow 0<|a|<1 wide If x-5 then h=+5 If x+5 then h=-5 h is the x value of the vertex. If +6 then k=6 If -6 then k=-6 k is the y value of the vertex.

Y= ax2 + bx + c Y= a (x - p) (x - q) Alg. 2 Notes: The Forms: Standard Form Y= ax2 + bx + c Use to find x value of vertex. Plug in for x and find y to get y value of the vertex. a>0 opens up a<0 opens down |a|>1 narrow 0<|a|<1 wide (0,c) is the y -intercept. The Forms: Intercept Form Y= a (x - p) (x - q) Example 1: Can we multiply? If so give dimensions of the answer. a>0 opens up a<0 opens down |a|>1 narrow 0<|a|<1 wide (p,0) and (q,0) are the x-intercepts. x-value of the vertex is (p+q)/2 y-value of vertex, plug in x and find y.

y = -2x2+2 b. y= -x2+4x-3 c. y= ½ (x+1)2 - 2 d. y= -2(x - 1)(x - 5) (4.1 & 4.2) Example 1: Graph. Label the vertex, axis of symmetry, and x-intercepts. Compare each to y=x2. Does it have a maximum or a minimum? y = -2x2+2 b. y= -x2+4x-3 c. y= ½ (x+1)2 - 2 d. y= -2(x - 1)(x - 5)

Example 1 (d). y= -2(x - 1)(x - 5) (4.1 & 4.2) Example 2: Change (c) and (d) from example 1 into standard form. Example 1(c). y= ½ (x+1)2 - 2 Example 1 (d). y= -2(x - 1)(x - 5) FOIL METHOD Words: 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

y = -2x2+2 b. y= -x2+4x-3 d. y= -2(x - 1)(x - 5) c. y= ½ (x+1)2 - 2 (4.1 & 4.2) Example 1: (answers) y = -2x2+2 b. y= -x2+4x-3 Maximum: (2,1) Axis of symmetry: x=2 x-intercepts: (1,0) & (3,0) Opens down, same width, vertex shifted right 2 units and up 1 unit. Maximum: (0,2) Axis of symmetry: x=0 x-intercepts: (-1,0) & (1,0) Opens down, narrower, vertex shifted up 2 units. d. y= -2(x - 1)(x - 5) c. y= ½ (x+1)2 - 2 Maximum: (3,8) Axis of symmetry: x=3 x-intercepts: (1,0) & (5,0) Opens down, narrower, vertex shifted right 3 units and up 8 units. Minimum: (-1,-2) Axis of symmetry: x=-1 x-intercepts: (-3,0) & (1,0) Opens up, wider, vertex shifted left 1 unit and down 2 units. (4.1 & 4.2) Example 2: (answers) d. y=-2x2 + 12x – 10 c. y= ½x2 + x – 3/2