Quadratics of the Form y = a(x – h) 2 + k stretch/compression reflection H. Shift left/right V. Shift up/down.

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Presentation transcript:

Quadratics of the Form y = a(x – h) 2 + k stretch/compression reflection H. Shift left/right V. Shift up/down

y = x 2 Opening: up/down Stretch: none/ stretched/ compressed Vertex: (0, 0) Horizontal shift Vertical shift 1) 2) 3) 4) 5) none

Equationopen stretch shrink left/rightup/down vertex 1y = 2x 2 2y = x 2 – 5 3y = (x + 4) 2 4y = – x y = x y = (x – 3) 2 up down up stretch normal left 4 right 3 down 5 up 5 up 3 (0,0) (0, –5) (–4,0) (0,5) (0,3) (3,0) no

Equationopen stretch shrink left/rightup/down vertex 7 8 y = –3(x + 2) 2 9 y = (x + 3) 2 – y = (x – 2) 2 – 4 12 down up down shrink stretch normal shrink normal shrink left 3 right 3 no down 5 down 4 (–2,0) (–3,–4) (1, –5) (2, –4) (3,6) left 2 right 1 right 2 no down 4 up 6

y = 2x 2 Opening: up/down Stretch: none/ stretched/ compressed Vertex: (0, 0) Horizontal Shift Vertical Shift 1) 2) 3) 4) 5) none (1)

y = x 2 – 5 Opening: up/down Stretch: none / stretched/ shrunk Vertex: (0, –5) Horizontal Shift Vertical Shift 1) 2) 3) 4) 5) none down 5 (2)

y = (x + 4) 2 Opening: up/down Stretch: none / stretched/ compressed Vertex: (– 4, 0) Horizontal shift Vertical shift 1) 2) 3) 4) 5) left 4 or (-4) none (3)

y = – x Opening: up/down Stretch: none / stretched/ compressed Vertex: (0, 5) Horizontal shift Vertical shift 1) 2) 3) 4) 5) none up 5 or (+5) (4)

y = x Opening: up/down Stretch: NONE/ stretched/ compressed Vertex: (0, 3) Horizontal shift Vertical shift 1) 2) 3) 4) 5) none up 3 or (+3) (5)

y = (x – 3) 2 Opening: up/down Stretch: NONE/ stretched/ compressed Vertex: (3, 0) Horizontal shift Vertical shift 1) 2) 3) 4) 5) right 3 or (+3) none (6)

Opening: up/down Stretch: NONE/ stretched/ compressed Vertex: (–2, 0) Horizontal shift Vertical shift 1) 2) 3) 4) 5) left 2 or (-2) none (7)

y = –3(x + 2) 2 Opening: up/down Stretch: NONE/ stretched/ compressed Vertex: (–2, 0) Horizontal shift Vertical shift 1) 2) 3) 4) 5) left 2 or (-2) none (8)

y = (x + 3) 2 – 4 Opening: up/down Stretch: NONE/ stretched/ compressed Vertex: (– 3,– 4) Horizontal shift Vertical shift 1) 2) 3) 4) 5) left 3 or (-3) down 4 or (-4) (9)

Opening: up/down Stretch: NONE/ stretched/ compressed Vertex: (1, – 5) Horizontal shift Vertical shift 1) 2) 3) 4) 5) right 1 or (+1) down 5 or (-5) (10)

y = (x – 2) 2 – 4 Opening: up/down Stretch: NONE/ stretched/ compressed Vertex: (2, – 4) Horizontal shift Vertical shift 1) 2) 3) 4) 5) right 2 or (+2) down 4 or (-4) (11)

Opening: up/down Stretch: NONE/ stretched/ compressed Vertex: (3, 6) Horizontal shift Vertical shift 1) 2) 3) 4) 5) right 3 or (+3) up 6 or (+6) (12)