For Exercises 9-16, a. Identify the equation as representing a circle, an ellipse, a hyperbola, or a parabola. b. Graph the curve. c. Identify key features of the graph. That is, If the equation represents a circle, identify the center and radius. If the equation represents an ellipse, identify the center, vertices, endpoints of the minor axis, foci, and eccentricity. If the equation represents a hyperbola, identify the center, vertices, foci, equations of the asymptotes, and eccentricity. If the equation represents a parabola, identify the vertex, focus, endpoints of the latus rectum, equation of the directrix, and equation of the axis of symmetry. − 9 x 2 + 16 y 2 + 64 y − 512 = 0
For Exercises 9-16, a. Identify the equation as representing a circle, an ellipse, a hyperbola, or a parabola. b. Graph the curve. c. Identify key features of the graph. That is, If the equation represents a circle, identify the center and radius. If the equation represents an ellipse, identify the center, vertices, endpoints of the minor axis, foci, and eccentricity. If the equation represents a hyperbola, identify the center, vertices, foci, equations of the asymptotes, and eccentricity. If the equation represents a parabola, identify the vertex, focus, endpoints of the latus rectum, equation of the directrix, and equation of the axis of symmetry. − 9 x 2 + 16 y 2 + 64 y − 512 = 0
Solution Summary: The author explains the nature of curve -9x2+16y2,+64y-512=0 among the types of circle, ellipse, hyperbola, or parabol
a. Identify the equation as representing a circle, an ellipse, a hyperbola, or a parabola.
b. Graph the curve.
c. Identify key features of the graph. That is,
If the equation represents a circle, identify the center and radius.
If the equation represents an ellipse, identify the center, vertices, endpoints of the minor axis, foci, and eccentricity.
If the equation represents a hyperbola, identify the center, vertices, foci, equations of the asymptotes, and eccentricity.
If the equation represents a parabola, identify the vertex, focus, endpoints of the latus rectum, equation of the directrix, and equation of the axis of symmetry.
4
For the function f(x) = 4e¯x, find f''(x). Then find f''(0) and f''(1).
Solve the next ED: (see image)
Write an equation for the polynomial graphed below. It will probably be easiest to leave your "a" value as a
fraction.
8
7
+
9+
H
6
5
4
3
+ 3
2
1
(-30)
(-1,0)
(1,0)
(3,0)
+
-5
-4
-3
-2
2
3
4
7 2
-1
-2
3 (0,-3)
f(x) =
456
-4
-5
-6+
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