1. Jeff Bivin -- LZHS Last Updated: April 7, 2011 By: Jeffrey Bivin Lake Zurich High School jeff.bivin@lz95.org

2. Jeff Bivin -- LZHS Graph the following parabola y = 3x 2 + 24x + 53 y = 3(x 2 + 8x ) + 53 y + 48 = 3(x 2 + 8x + (4) 2 ) + 53 y = 3(x + 4) 2 + 5 Axis of symmetry: x = -4 Vertex: (-4, 5) y = 3(x 2 + 8x + (4) 2 ) + 53 - 48 3●(4) 2 = 48 x + 4 = 0 Note: opens up

3. Jeff Bivin -- LZHS Graph the following parabola y = 3(x + 4) 2 + 5 No x-intercept y-intercept: x-intercept none y-intercept

4. Jeff Bivin -- LZHS Graph the following parabola y = -2x 2 + 12x + 11 y = -2(x 2 - 6x ) + 11 y - 18 = -2(x 2 - 6x + (-3) 2 ) + 11 y = -2(x - 3) 2 + 29 Axis of symmetry: x = 3 Vertex: (3, 29) y = -2(x 2 - 6x + (-3) 2 ) + 11 + 18 -2●(-3) 2 = -18 x - 3 = 0 Note: opens down

5. Jeff Bivin -- LZHS Graph the following parabola y = -2(x - 3) 2 + 29 x-intercept y-intercept

6. Jeff Bivin -- LZHS Graph the following parabola x = -2y 2 - 8y - 1 x = -2(y 2 + 4y ) - 1 x - 8 = -2(y 2 + 4y + (2) 2 ) - 1 x = -2(y + 2) 2 + 7 Axis of symmetry: y = -2 Vertex: (7, -2) x = -2(y 2 + 4y + (2) 2 ) - 1 + 8 -2(2) 2 = -8 y + 2 = 0 Note: opens left

7. Jeff Bivin -- LZHS Graph the following parabola x = -2(y + 2) 2 + 7 y-intercept

8. Jeff Bivin -- LZHS Graph the following parabola x = y 2 - 4y + 11 x = (y 2 - 8y ) + 11 x + 8 = (y 2 - 8y + (-4) 2 ) + 11 x = (y - 4) 2 + 3 Axis of symmetry: y = 4 Vertex: (3, 4) x = (y 2 - 8y + (-4) 2 ) + 11 - 8 y - 4 = 0 Note: opens right

9. Jeff Bivin -- LZHS Graph the following parabola y-intercept x-intercept

10. Jeff Bivin -- LZHS Graph the following parabola x = y 2 + 10y + 8 x = (y 2 + 10y ) + 8 x + 25 = (y 2 + 10y + (5) 2 ) + 8 x = (y + 5) 2 - 17 Axis of symmetry: y = -5 Vertex: (-17, -5) x = (y 2 + 10y + (5) 2 ) + 8 - 25 (5) 2 = 25 y + 5 = 0 Note: opens right

11. Jeff Bivin -- LZHS Graph the following parabola x = (y + 5) 2 - 17 y-intercept x-intercept

12. Jeff Bivin -- LZHS Graph the following parabola y = 5x 2 - 30x + 46 y = 5(x 2 - 6x ) + 46 y + 45 = 5(x 2 - 6x + (-3) 2 ) + 46 y = 5(x - 3) 2 + 1 Axis of symmetry: x = 3 Vertex: (3, 1) y = 5(x 2 - 6x + (-3) 2 ) + 46 - 45 5●(-3) 2 = 45 x - 3 = 0 Note: opens up

13. Jeff Bivin -- LZHS Graph the following parabola y = 5(x - 3) 2 + 1 x-intercept y-intercept