Warm-Up 1/08Identify the vertex, focus, axis of symmetry and directrix of the equation (y + 5)² = 24(x – 1).

h = 1; k = – 5; p = 6 vertex: (1, – 5)focus: (7, – 5)AS: y = – 5DX: x = – 5

Rigor:You will learn how to analyze and graph equations of parabolas and how to write

equations of parabolas.

Relevance:You will be able to use graphs and equations of

parabolas to solve real world problems.

7-1b Parabolas

Example 4a: Write an equation for and graph a parabola with the give Characteristics.

focus and vertex

h=1¿ (1 ,− 4 )𝑘=− 4

1+𝑝=3𝑝=2

graph opens rightvertex

focus ¿ (3 ,− 4 )

x y

1 – 4 18

(𝑦+4 )2

=𝑥−1

18

(𝑦+4 )2

+1=𝑥

03

49

– 83

– 129

(𝑦−𝑘)2=4𝑝 (𝑥− h )(𝑦−− 4 )2=4 (2 ) (𝑥− 1 )

(𝑦+4 )2=8 (𝑥−1 )

Example 4b: Write an equation for and graph a parabola with the give Characteristics.

vertex , directrix y = 1

h=− 2¿ (− 2 ,4 )𝑘=4

1=4 −𝑝𝑝=3

graph opens upvertex

directrix 𝑦=1

x y

–2 4 112

(𝑥+2 )2

=𝑦− 4

112

(𝑥+2 )2

+4=𝑦

77

1610

7–8

16– 14

(𝑥− h )2=4𝑝 (𝑦−𝑘 )

(𝑥+2 )2=12 (𝑦− 4 )(𝑥−− 2 )2=4 (3 ) (𝑦− 4 )

Example 4c: Write an equation for and graph a parabola with the give Characteristics.

focus , opens left, contains

h=2 −𝑝¿ (2 ,5 )

𝑘=1h+𝑝=2

𝑦=5point

focus ¿ (2 ,1 )

x y

4 1

−18

( 𝑦− 1 )2

=𝑥− 4

−18

( 𝑦− 1 )2

+4=𝑥

52

9– 4

– 32

– 7– 4

(𝑦−𝑘)2=4𝑝 (𝑥− h )(5 −1 )2=4𝑝 ( 2− (2−𝑝 ) )

1 6=4𝑝2

𝑥=2

(𝑦−1 )2=4 (−2 ) (𝑥− 4 )

4=𝑝2

± 2=𝑝−2=𝑝h=4

(𝑦−𝑘)2=4𝑝 (𝑥− h )

(𝑦−1 )2=− 8 (𝑥− 4 )

Example 5: Write an equation for the line tangent to at C(7, 2).

graph opens right

h=3 𝑘=04𝑝=1𝑝=.25

¿ (3 ,0 )vertexfocus ¿ (3.25 ,0 )

𝑑=√ (𝑥2−𝑥1 )2+( 𝑦2− 𝑦1 )2

𝑑=4.25𝑑=√ (7−3.25 )2+(2−0 )2

𝐴 (3.25− 4.25 ,0 )𝐴 (− 1 , 0 )𝑚=

2− 07− (−1 )

=14

y − 𝑦1=𝑚 (𝑥−𝑥1 )

y −0=14

(𝑥− (−1 ) )

y=14𝑥+

14

√−1math!

7-1a Assignment: TX p428, 28-48 EOE only graph 28 & 32