1. Projects are due
ACT Questions?

2. Guided Notes for Unit 4-4: Hyperbola
Learning Target:
I will graph hyperbolas.

4. HYPERBOLA TERMS Vertex EQUATION FORM CENTER The “Butterfly” VERTICES
CO-VERTICES
ASYMPTOTES
(h, k )
(h ± a , k)
Co-vertex
(h, k ± b )
Vertex b a
Vertex
C=(h , k)
Co-vertex

5. HYPERBOLA TERMS Vertex EQUATION FORM CENTER The “Hourglass” VERTICES
CO-VERTICES
ASYMPTOTES
(h, k )
Vertex
(h, k ± a )
(h ± b, k)
C=(h , k)
Co-vertex a b
Co-vertex
Vertex

6. Example 1 The equation of the form 𝑥−ℎ 2 𝑎 2 − 𝑦−𝑘 2 𝑏 2 =1, so
Graph 4x2 – 16y2 = 64.
4x2 – 16y2 = 64
– = 1 Rewrite the equation in standard form.
x 2 16
y 2 4
Since a2 = 16 and b2 = 4, a = 4 and b = 2.
The equation of the form 𝑥−ℎ 2 𝑎 2 − 𝑦−𝑘 2 𝑏 2 =1, so
Step 1: Graph the vertices. Since the transverse axis is horizontal, the vertices lie on the x-axis. The coordinates are (±a, 0), or (±4, 0).
Step 2: Use the values a and b to draw the central “invisible” rectangle. The lengths of its sides are 2a and 2b, or 8 and 4.

7. Example 1
Graph 4x2 – 16y2 = 64.
Step 3: Draw the asymptotes. The equations of the asymptotes are 𝑦=𝑘 ± 𝑏 𝑎 𝑥−ℎ , which comes out to be 𝑦 = 1 2 𝑥 and 𝑦 = − 1 2 𝑥 the asymptotes contain the diagonals of the central rectangle.
Step 4: Sketch the branches of the hyperbola through the vertices so they approach the asymptotes.

8. Graph and Label b) Find coordinates of vertices, covertices a) GRAPH
Center = (-5,-2)
Butterfly shape since the x terms come first
Since a = 2 and b = 3
Vertices are 2 points left and right from center  (-5 ± 2, -2)
CoVertices are 3 points up and down  (-5, -2 ± 3)
a) GRAPH
Plot Center (-5,-2)
a = 2 (go left and right)
b = 3 (go up and down)

9. Graph and Label b) Find coordinates of vertices, covertices, a) GRAPH
Center = (-1,3)
Hourglass shape since the y terms come first
Since a = 2 and b = 4
Vertices are 2 points up and down from center  (-1, 3 ± 2)
Covertices are 3 points left and right  (-1 ± 4, 3)
a) GRAPH
Plot Center (-1,3)
a = 2 (go up and down)
b = 4 (go left and right)

10. Assignment
Pg. 629 #16-19