Unit 1 – Conic SectionsSection 1.3 – The Parabola

Calculator Required

2y 4k hxp 2

x 4h kyp

Vertex: (h, k)

Opens Left/Right Opens Up/Down

Vertex: (h, k)

Focus: h kp, Focus: h, k p

Directrix: x ph Directrix: y pk

Axis of Sym: y k Axis of Sym: x h

V

p

2p2pF

p

Directrix

Vp

2p

2p

Fp

Directrix

Given the equation 2x 8ya) Write the equation in standard form

2x 4h kyp 2

x y0 024

V

F

b) Provide the appropriate information.

Focus: (0, 2)Vertex: (0, 0)

Directrix: y = -2Axis of Sym: x = 0

c) Graph the equation

Given the equation 2y 8x 4y 20 0 a) Write the equation in standard form

2y 4y 8x 20 2 4 4y 4y 8x 20

2y 82 x 16

22x2y 8

2y 42 2x2

Given the equation 2y 8x 4y 20 0 a) Write the equation in standard form

2y 4y 8x 20 2y x2 224

V

F

b) Provide the appropriate information.

Focus: (4, 2)Vertex: (2, 2)

Directrix: x = 0Axis of Sym: y = 2

c) Graph the equation

Given the equation 2x 6x 8y 7 0 a) Write the equation in standard form

2x 6x 8y 7 2 9 9x 6x 8y 7

2y 63x 8 1

2283x y

2x 43 y2 2

Given the equation 2x 6x 8y 7 0 a) Write the equation in standard form

2x 6x 8y 7 0 2x 43 2y2

V

F

b) Provide the appropriate information.

Focus: (3, 0)Vertex: (3, 2)

Directrix: y = 4Axis of Sym: x = 3

c) Graph the equation

Write the equation of the parabola with focus at (2, 2)and directrix x = 4

F

V

2y 4k hxp

2y 42 x1 3

242 3y x

Write the equation of the parabola with V(-1, -3) and F(-1, -6)

V

F

2x 4h kyp

2x 4 31 3y

221 3x y1