ACT Questions Learning Target I will graph hyperbolas

ACT Questions?

Learning Target: I will graph hyperbolas.

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

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

Graph 4 x 2 – 16 y 2 = 64 y 2 x 2 – = 1 Rewrite the equation in standard form. 16 4 Since a 2 = 16 and b 2 = 4, a = 4 and b = 2. Step 1: Graph the vertices. Since the transverse axis is horizontal, the vertices lie on the xaxis. 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 2 a and 2 b, or 8 and 4.

Graph 4 x 2 – 16 y 2 = 64. Step 4: Sketch the branches of the hyperbola through the vertices so they approach the asymptotes.

§ b) Find coordinates of vertices, covertices § 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) § Co. Vertices 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)

§ b) Find coordinates of vertices, covertices, § 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)

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