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mathematics
college algebra graphs and models

Questions and Answers of College Algebra Graphs And Models

Graph the ellipse. Label the foci and the endpoints of each axis. 25x² +9y² = 225
Sketch a graph of the parabola. x = f
Match the equation with its graph (a-f). 4 1
Sketch a graph of the hyperbola, including the asymptotes. Give the coordinates of the foci and vertices. 4x² - 4y² = 100
Sketch a graph of the parabola. 4x² = -2y
Match the equation with its graph (a-f). 36 25 = 1
Match the equation with its graph (a-d). C. 7 -2 2 2 b. d. O 7 7 9
Graph the ellipse. Label the foci and the endpoints of each axis. 5x² + 4y² = 20
Sketch a graph of the parabola. y² = -3x
Match the equation with its graph (a-d). 이집 2²-2²2²- _ 6 4
Sketch a graph of the parabola. y² = -4x
Sketch a graph of the parabola. x² = 4y
Match the equation with its graph (a-d). C. 7 -2 2 2 b. d. O 7 7 9
Match the equation with its graph (a-d). 9 . y2 = 1
Sketch a graph of the parabola. Hx- = ܐy
Match the equation with its graph (a-d). C. 7 -2 2 2 b. d. O 7 7 9
Match the equation with its graph (a-d). 9 16 1
Determine an equation of the conic section that satisfies the given conditions.Parabola with focus (2, 0) and vertex (0, 0)
Match the equation with its graph (a-d). 2-2=1
Determine an equation of the conic section that satisfies the given conditions.Parabola with vertex (5,2) and focus (5,0)
Determine an equation of the conic section that satisfies the given conditions.Ellipse with foci (±4,0) and vertices (±5, 0)
Determine an equation of the conic section that satisfies the given conditions.Ellipse centered at the origin with vertical major axis of length 14 and minor axis of length 8
Determine an equation of the conic section that satisfies the given conditions.Hyperbola with foci (0, ±10) and endpoints of the conjugate axis (±6,0)
Match the equation with its graph (a-d). C. 7 -2 2 2 b. d. O 7 7 9
Sketch a graph of the parabola. 8x = y²
Find the standard equation of the ellipse shown in the figure. Identify the coordinates of the vertices, endpoints of the minor axis, and the foci. 3
Sketch a graph of the conic section. Give the coordinates of any foci. zx = 4+-
Sketch a graph of a hyperbola, centered at the origin, with the foci, vertices, and asymptotes shown in the figure. Find an equation of the hyperbola. (The coordinates of the foci and vertices are
Sketch a graph of the conic section. Give the coordinates of any foci. J² = 8x
Find the standard equation of the ellipse shown in the figure. Identify the coordinates of the vertices, endpoints of the minor axis, and the foci. 딤 4
Match the equation with its graph (a-f). x² = -2y
Sketch a graph of a hyperbola, centered at the origin, with the foci, vertices, and asymptotes shown in the figure. Find an equation of the hyperbola. (The coordinates of the foci and vertices are
The foci F1 and F2, vertices V1 and V2, and endpoints U1 and U2 of the minor axis of an ellipse are labeled in the figure. Graph the ellipse and find its standard equation. (The coordinates of V1,
Find the standard equation of the ellipse shown in the figure. Identify the coordinates of the vertices, endpoints of the minor axis, and the foci. -6 2 7 2 6 x.
Match the equation with its graph (a-f). -8.x
Match the equation with its graph (a-f). xp = (
Sketch a graph of the conic section. Give the coordinates of any foci. +2²=1 25 4
The foci F1 and F2, vertices V1 and V2, and endpoints U1 and U2 of the minor axis of an ellipse are labeled in the figure. Graph the ellipse and find its standard equation. (The coordinates of V1,
Sketch a graph of the conic section. Give the coordinates of any foci. 49x²+36y² = 1764
Match the equation with its graph (a-f). x= ܫܠܨ
Determine an equation of the hyperbola, centered at the origin, satisfying the conditions. Give the equations of its asymptotes. Foci (0, 13), vertices (0, 12)
Determine an equation of the hyperbola, centered at the origin, satisfying the conditions. Give the equations of its asymptotes. Foci (±13, 0), vertices (±5, 0)
The foci F1 and F2, vertices V1 and V2, and endpoints U1 and U2 of the minor axis of an ellipse are labeled in the figure. Graph the ellipse and find its standard equation. (The coordinates of V1,
Match the equation with its graph (a-f). y = -2x²
Sketch a graph of the conic section. Give the coordinates of any foci. 16 9 = 1
Determine an equation of the hyperbola, centered at the origin, satisfying the conditions. Give the equations of its asymptotes. Vertical transverse axis of length 4, foci (0, ±5)
Sketch a graph of the conic section. Give the coordinates of any foci. 1=ܐ . 4 ܐ
The foci F1 and F2, vertices V1 and V2, and endpoints U1 and U2 of the minor axis of an ellipse are labeled in the figure. Graph the ellipse and find its standard equation. (The coordinates of V1,
Graph the parabola. Label the vertex, focus, and directrix. 16y = x²
Graph the parabola. Label the vertex, focus, and directrix. y = -2x²
Determine an equation of the hyperbola, centered at the origin, satisfying the conditions. Give the equations of its asymptotes. Horizontal transverse axis of length 12, foci (± 10, 0)
Graph the parabola. Label the vertex, focus, and directrix. x = ?
Sketch a graph of the conic section. Identify the coordinates of its center when appropriate. (y-2)²(x + 1)² + 4 16 1
Sketch a graph of the conic section. Identify the coordinates of its center when appropriate. (x − 1)² _ (y + 1)² 4 4 1
Determine an equation of the hyperbola, centered at the origin, satisfying the conditions. Give the equations of its asymptotes. Vertices (0, ±4), asymptotes y = ±x
Sketch a graph of the conic section. Identify the coordinates of its center when appropriate. (x + 2) = 4(y - 1)²
Graph the parabola. Label the vertex, focus, and directrix. -y² = 6x
Find an equation of the ellipse, centered at the origin, satisfying the conditions.Foci (0, ±2), vertices (0, ±4)
Determine an equation of the hyperbola, centered at the origin, satisfying the conditions. Give the equations of its asymptotes. Endpoints of conjugate axis (0, ±3), vertices (±4,0)
Graph the parabola. Label the vertex, focus, and directrix. d = xt-
Determine an equation of the hyperbola, centered at the origin, satisfying the conditions. Give the equations of its asymptotes. Endpoints of conjugate axis (±4,0), vertices (0, ±2)
Find an equation of the ellipse, centered at the origin, satisfying the conditions.Foci (0, ±3), vertices (0, ±5)
Sketch a graph of the conic section. Give the coordinates of any foci. (x - 3)² + (y + 1)² = 9
Find an equation of the ellipse, centered at the origin, satisfying the conditions.Foci (±5, 0), vertices (±6, 0)
Find an equation of the ellipse, centered at the origin, satisfying the conditions.Foci (±4,0), vertices (±6, 0)
Determine an equation of the hyperbola, centered at the origin, satisfying the conditions. Give the equations of its asymptotes. Vertices (±3,0), asymptotes y = ±x
Graph the equation. RIFFE = 24
Determine an equation of the hyperbola, centered at the origin, satisfying the conditions. Give the equations of its asymptotes. Vertices (± √10,0), passing through (10, 9)
Graph the equation. 7.1x² + 8.2y² = 60
Sketch a graph of the hyperbola. Identify the vertices, foci, and asymptotes. (x - 1)²_ (y-2)² 16 4
Graph the parabola. Label the vertex, focus, and directrix. x² = -4y
Determine an equation of the hyperbola, centered at the origin, satisfying the conditions. Give the equations of its asymptotes. Vertices (0, + √5), passing through (4, 5)
Graph the equation. (y-1.4)² 7 (x+2.3)² 11 1
Graph the parabola. Label the vertex, focus, and directrix. 2y² = -8x
Find an equation of the ellipse, centered at the origin, satisfying the conditions. Eccentricity, horizontal major axis of length 6
Sketch a graph of the hyperbola. Identify the vertices, foci, and asymptotes. (y + 1)² _ (x + 3)² 16 9
Find an equation of the ellipse, centered at the origin, satisfying the conditions. Eccentricity, vertices (0, ±8)
Sketch a parabola with focus and directrix as shown in the figure. Find an equation of the parabola. F(0, 1) y=-1
Find an equation of the ellipse, centered at the origin, satisfying the conditions.Horizontal major axis of length 8, minor axis of length 6
Graph the parabola. Label the vertex, focus, and directrix. -3x = y²
Sketch a graph of the hyperbola. Identify the vertices, foci, and asymptotes. - 2)²(x + 2)² 36 4 1
Write the equation in the form given by (y - k)2 = a (x - h). -2x = y² + 8x + 14
Sketch a graph of the hyperbola. Identify the vertices, foci, and asymptotes. (x + 1)² _ (y − 1)² 4 4 = 1
Translate the ellipse with the given equation so that it is centered at the given point. Find the new equation and sketch its graph. 4 + 3 = 1; (2, -1)
Sketch a parabola with focus and directrix as shown in the figure. Find an equation of the parabola. -5-3 y = 2 35 F(0, -2)
Find an equation of the ellipse, centered at the origin, satisfying the conditions.Vertical major axis of length 12, minor axis of length 8
Write the equation in the form given by (y - k)2 = a (x - h). 2y² 12y + 16 = x -
Sketch a graph of the hyperbola. Identify the vertices, foci, and asymptotes. * - (y - (y – 1)2 = 1 4
Translate the ellipse with the given equation so that it is centered at the given point. Find the new equation and sketch its graph. + 9 = 1; (-3,7)
Sketch a parabola with focus and directrix as shown in the figure. Find an equation of the parabola. F(-3,0) ** 2 |x = 3
Translate the ellipse with the given equation so that it is centered at the given point. Find the new equation and sketch its graph. 2 10 9 1; (-3,-4)
Graph the parabola. Label the vertex, focus, and directrix. = ² - 3x =
Graph the parabola. Label the vertex, focus, and directrix. x² = -8y
Sketch a graph of (y - 4)2 = -8(x-8). Include the focus and the directrix.
Sketch a parabola with focus and directrix as shown in the figure. Find an equation of the parabola. x=-0.5 F(0.5, 0)
Use mathematical induction to prove the statement. Assume that n is a positive integer. 3+6+9+ + 3n = 3n(n + 1) 2
Use mathematical induction to prove the statement. Assume that n is a positive integer. 4+7+ 10 ++ (3n+ 1): + (3n + 1) = n (3n + 5) 2
Use mathematical induction to prove the statement. Assume that n is a positive integer. 5 + 10 + 15 + + 5n 5n(n + 1) 2
Complete the following. (a) Write the described sequence. (b) Write a series that sums the terms of the sequence in part (a). (c) Find the sum of the series in part (b).The integers
Use mathematical induction to prove the statement. Assume that n is a positive integer. 3+3² +3³ + +3": 3(3" - 1) 2

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