College Algebra
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The following equation is that of a parabola. Using its vertex and the direction in which it opens, solve for its domain and range, and tell if the given relation is a function or not.
x = - 8(y - 5)2 + 9
y = - x2 + 10x - 21
y2 + 4y - x - 3 = 0
Write the equation of the parabola in standard form given the following conditions.
Focus (- 1, 5), Directrix: y = 3
Focus (6, 1), Directrix: x = - 4
Vertex: (1, - 4); Focus: (1, - 9)
Focus (0, - 10), Directrix: y = 10
Focus (0, 12), Directrix: y = - 12
Focus: (- 11, 0); Directrix: x = 11
Focus: (3, 0); Directrix: x = - 3
Without completing the square, determine the given equation.x2 -2x -4y +29 =0
A nondegenerate conic section of the form is given. Distinguish the conic section represented, without completing the square. 4x2- y2/6 + 8x + 3y = 0
A nondegenerate conic section of the form is given. Distinguish the conic section represented, without completing the square. x2+4y2+2x+4y+6 = 0
Consider the given conditions for a parabola and find the standard form of the equation. Focus: (0, 6); Directrix: y = -6
Consider the given conditions for a parabola and find the standard form of the equation. Focus: (-3, 0); Directrix: x =3
Draw the parabola on the coordinate system after finding the vertex, focus, and directrix of the parabola. y2 = 16x
Draw the parabola on the coordinate system after finding the vertex, focus, and directrix of the parabola. (y+1)2= -4x
Draw the parabola on the coordinate system after finding the vertex, focus, and directrix of the parabola. (x+2)2= 4(y-2)
Draw the parabola on the coordinate system after finding the vertex, focus, and directrix of the parabola. x2 -10x + 4y = 29
Choose the correct option for the graph, focus, and directrix of the parabola.y2 = 8x
Choose the correct option for the graph, focus, and directrix of the parabola.x2 = 8y
Choose the correct option for the graph, focus, and directrix of the parabola.x2 = -8y
Choose the correct option for the graph, focus, and directrix of the parabola.y2 = -8x
For the following equation of a parabola, solve for the focus and directrix, and then graph.
y2 = 24x
y2 = - 24x
x2 = 24y
x2 = - 24y
y2 - 44x = 0
18x2 + 9y = 0
Choose the correct option for the vertex, directrix, focus, and graph of the parabola.(y - 9)2 = 16(x - 3)
Choose the correct option for the vertex, directrix, focus, and graph of the parabola.(x +9)2 = - 16(y + 3)
Choose the correct option for the vertex, directrix, focus, and graph of the parabola.
(y - 9)2 = -16(x - 3)
Using the provided equation, find the parabola's vertex, focus, and directrix. Then, graph the parabola.(x - 7)2 = 12(y - 3)
By graphing the given system in the same rectangular coordinate system and finding the intersection points, find the solution set and verify the solution.y = x2 +11y = x2 -11x
By graphing the given system in the same rectangular coordinate system and finding the intersection points, find the solution set and verify the solution.y = (x -9)2 -7(x -9)2 + (y -10)2 = 9
Using the provided equation, find the parabola's vertex, focus, and directrix. Then, graph the parabola.(x + 5)2 = - 12(y + 2)
Using the provided equation, find the parabola's vertex, focus, and directrix. Then, graph the parabola.(y + 8)2 = 8(x + 6)
Using the provided equation, find the parabola's vertex, focus, and directrix. Then, graph the parabola.(y + 9)2 = - 4x
By completing the square, write the given equation into the standard form, and then identify the vertex, focus, and directrix of the parabola. Also, graph the parabola in a rectangular coordinate system.x2 - 4x - 4y +16 =0
By completing the square, write the given equation into the standard form, and then identify the vertex, focus, and directrix of the parabola. Also, graph the parabola in a rectangular coordinate system.y2 - 6y + 8x +41 = 0
By completing the square, write the given equation into the standard form, and then identify the vertex, focus, and directrix of the parabola. Also, graph the parabola in a rectangular coordinate system.x2 + 10x - 12y + 13 = 0
By graphing the given system in the same rectangular coordinate system and finding the intersection points, find the solution set and verify the solution.(y-7)2 = x +19y = x -4