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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