UNIT 4 DAY 9 HOMEWORK: Quadratic Functions in Standard and Vertex Form, Analyzing Quadratic Functions Find the axis of symmetry, the coordinates of the vertex, and then graph the function. 1. y = 1/3 * (x + 3) ^ 2 - 1 Vertical compression by a factor of Transformations: Translation loft 3 units and down / unit Axis of Symmetry: x = - 3 Vertex: (-3,-1) 2. y = x ^ 2 + 4x + 4 (Hint: (Hint: x = (- b)/(2a) find the axis of symmetry) Axis of Symmetry: X = - 2 x = - 4/(2 * 1) (-2,0) Vertex: Y(- 2) = (- 2) ^ 2 + 4(- 2) + 4 Zeros: -2 4 y-intercept: x ^ 2 + 4x + 4 =0 Rightarrow x=-2 Y(0) = y Given the function described, write the equation of the function in vertex form, and then state the vertex, and the axis of symmetry. 3. A quadratic function vertically compressed by a factor of 1/2 and reflected over the x-axis. Equation: y = - 1/2 * x ^ 2 Vertex: (0,0) Axis of Symmetry: x = 0 4. A quadratic function shifted to the right 4 and shifted up 7. Equation: y = (x - 4) ^ 2 + 7 Vertex (4,7) Axis of Symmetry: x = 4 5. A quadratic function reflected over the x-axis, vertically stretched by a factor of 3, shifted left 2 and down 10. Equation: y = - 3 * (x + 2) ^ 2 - 10 Vertex:(-2,-10) Axis of Symmetry: x = - 2 2 2 Graph and analyze the quadratic functions. 6. y = - 1/2 * (x - 3) ^ 2 + 8 A. Domain: (- ∞, ∞) Flenge: (-00, 8 B. LEB: Asy-00, y-00 REB: As X, Y-00 C. x-intercepts: - 1.17/(7/2) y-intercept: D. Vertex (3,8) 8 (loral and global) E. Int. of Inc: (- ∞, 3) Int. of Dec: (3,00) -(x3)²+8=0⇒x=-land 7; 410)=-210-3)² +8=3 7. y = x ^ 2 + 5x - 2 A.(-00,00) Range: [-34,00) B. LEB: ASX-00, 40 Asx 00, Y intercepts: REB: -5-153 and 5+133 -5372 and 0.372 y--2 D. Vertex: (- 5/3, - 33/4) ar(ln) - 33/4 (laralandglabal) E. int (- 5/2, ∞) Int. of Dec: (- ∞, - 5/2) x=- S 2* i Rightarrow x = - 5/2 . Y(- 5/2) = (- 5/2) ^ 2 + 5(- 5/2) - 2 = - 33/4 Y(0) = 0 ^ 2 + 5 * 0 - 2 = - 2 x ^ 2 + 5x - 2 = 0 3 Since alpha > 0 there are 2 distinct real solutions to the quadratic equation. d = 5 ^ 2 - 4 * 1(- 2) = 33 Since & is not a perfect square, the qualiclic exposetion is prime over the integers. 3 x = (- 5 plus/minus sqrt(33))/(2 * 1) = (- S plus/minus sqrt(33))/2