jeff bivin -- lzhs last updated: april 7, 2011 by: jeffrey bivin lake zurich high school...
TRANSCRIPT
Jeff Bivin -- LZHSLast Updated: April 7, 2011
By: Jeffrey BivinLake Zurich High School
Jeff Bivin -- LZHS
Graph the following parabola
y = 3x2 + 24x + 53
y = 3(x2 + 8x ) + 53
y + 48 = 3(x2 + 8x + (4)2) + 53
y = 3(x + 4)2 + 5
Axis of symmetry: x = -4
Vertex: (-4, 5)
y = 3(x2 + 8x + (4)2) + 53 - 48
3●(4)2 = 48
x + 4 = 0
Note: opens up
Jeff Bivin -- LZHS
Graph the following parabolay = 3(x + 4)2 + 5
No x-intercept
y-intercept:
23 0 24 0 53 53y
x-intercept
none
y-intercept
0, 53
Jeff Bivin -- LZHS
Graph the following parabola
y = -2x2 + 12x + 11
y = -2(x2 - 6x ) + 11
y - 18 = -2(x2 - 6x + (-3)2) + 11
y = -2(x - 3)2 + 29
Axis of symmetry: x = 3
Vertex: (3, 29)
y = -2(x2 - 6x + (-3)2) + 11 + 18
-2●(-3)2 = -18
x - 3 = 0
Note: opens down
Jeff Bivin -- LZHS
Graph the following parabolay = -2(x - 3)2 + 29
x-intercept
y-intercept
22 0 3 29y
0, 11
20 2 3 29x
229 2 3x
2292 3x
292 3x
2923 x
5823 , 0
36.808, 0 & .808, 0
11y
Jeff Bivin -- LZHS
Graph the following parabola
x = -2y2 - 8y - 1
x = -2(y2 + 4y ) - 1
x - 8 = -2(y2 + 4y + (2)2) - 1
x = -2(y + 2)2 + 7
Axis of symmetry: y = -2
Vertex: (7, -2)
x = -2(y2 + 4y + (2)2) - 1 + 8
-2(2)2 = -8
y + 2 = 0
Note: opens left
Jeff Bivin -- LZHS
Graph the following parabolax = -2(y + 2)2 + 7
y-intercepty-intercept
22 0 2 7x
1, 0
20 2 2 7y
27 2 2y
272 2y
72 2y
722 y
1420, 3
4.871, 0 & 1.129, 0
8 7x
Jeff Bivin -- LZHS
Graph the following parabola
x = y2 - 4y + 11
x = (y2 - 8y ) + 11
x + 8 = (y2 - 8y + (-4)2) + 11
x = (y - 4)2 + 3
Axis of symmetry: y = 4
Vertex: (3, 4)
x = (y2 - 8y + (-4)2) + 11 - 82
12
12
1
2
1
2
1
8)16(2
1
y - 4 = 0
Note: opens right
Jeff Bivin -- LZHS
Graph the following parabola 21
4 32
x y
y-interceptx-intercept
210 4 3
2x
11, 0
none
8 3x 11x
Jeff Bivin -- LZHS
Graph the following parabola
x = y2 + 10y + 8
x = (y2 + 10y ) + 8
x + 25 = (y2 + 10y + (5)2) + 8
x = (y + 5)2 - 17
Axis of symmetry: y = -5
Vertex: (-17, -5)
x = (y2 + 10y + (5)2) + 8 - 25
(5)2 = 25
y + 5 = 0
Note: opens right
Jeff Bivin -- LZHS
Graph the following parabolax = (y + 5)2 - 17
y-interceptx-intercept
20 5 17x
8, 0
20 5 17y
217 5y
17 5y
5 17 y
0, 5 17
0.877, 0 & 9.123, 0
25 17x 8x
Jeff Bivin -- LZHS
Graph the following parabola
y = 5x2 - 30x + 46
y = 5(x2 - 6x ) + 46
y + 45 = 5(x2 - 6x + (-3)2) + 46
y = 5(x - 3)2 + 1
Axis of symmetry: x = 3
Vertex: (3, 1)
y = 5(x2 - 6x + (-3)2) + 46 - 45
5●(-3)2 = 45
x - 3 = 0
Note: opens up
Jeff Bivin -- LZHS
Graph the following parabolay = 5(x - 3)2 + 1
x-intercept y-intercept
25 0 3 1y
0, 46
none
45 1y