Question 1

Given the quadratic function in vertex form

y = 2(x - 3)^2 + 4

, what is the vertex, axis of symmetry, focus, and directrix?

Accepted Answer

Vertex: (3, 4); Axis of Symmetry: x = 3; Focus: (3, 4.25); Directrix: y = 3.75

Answer

Vertex: (3, 4); Axis of Symmetry: x = 4; Focus: (3, 4.5); Directrix: y = 3.5

Answer

Vertex: (-3, 4); Axis of Symmetry: x = -3; Focus: (-3, 4.25); Directrix: y = 3.75

Answer

Vertex: (3, -4); Axis of Symmetry: x = 3; Focus: (3, -3.75); Directrix: y = -4.25

Question 2

For the parabola given by the equation

y = 2(x - 3)^2 + 4

, identify the vertex, axis of symmetry, focus, and directrix.

Accepted Answer

Vertex: (-2, 5); Axis of Symmetry: x = -2; Focus: (-2, 4.9167); Directrix: y = 5.0833

Answer

Vertex: (2, 5); Axis of Symmetry: x = 2; Focus: (2, 4.9167); Directrix: y = 5.0833

Answer

Vertex: (-2, -5); Axis of Symmetry: x = -2; Focus: (-2, -4.9167); Directrix: y = -5.0833

Answer

Vertex: (-2, 5); Axis of Symmetry: x = -2; Focus: (-2, 5.0833); Directrix: y = 4.9167

Question 3

Consider the parabola described by the equation

y = 2(x - 3)^2 + 4

. What are the vertex, axis of symmetry, focus, and directrix?

Accepted Answer

Vertex: (4, -3); Axis of Symmetry: x = 4; Focus: (4, -2.75); Directrix: y = -3.25

Answer

Vertex: (-4, -3); Axis of Symmetry: x = -4; Focus: (-4, -2.75); Directrix: y = -3.25

Answer

Vertex: (4, -3); Axis of Symmetry: y = 4; Focus: (4, -3.25); Directrix: x = -2.75

Answer

Vertex: (4, 3); Axis of Symmetry: x = 4; Focus: (4, 2.75); Directrix: y = 3.25

Question 4

Find the vertex, axis of symmetry, focus, and directrix for the parabola represented by the equation

y = 2(x - 3)^2 + 4

.

Accepted Answer

Vertex: (1, 6); Axis of Symmetry: x = 1; Focus: (1, 5.875); Directrix: y = 6.125

Answer

Vertex: (-1, 6); Axis of Symmetry: x = -1; Focus: (-1, 5.875); Directrix: y = 6.125

Answer

Vertex: (1, 6); Axis of Symmetry: x = 0; Focus: (1, 6.125); Directrix: y = 5.875

Answer

Vertex: (1, -6); Axis of Symmetry: x = 1; Focus: (1, -5.875); Directrix: y = -6.125

Question 5

Identify the vertex, axis of symmetry, focus, and directrix for the parabola described by

y = 2(x - 3)^2 + 4

.

Accepted Answer

Vertex: (-3, -7); Axis of Symmetry: x = -3; Focus: (-3, -6.9375); Directrix: y = -7.0625

Answer

Vertex: (-3, 7); Axis of Symmetry: x = -3; Focus: (-3, 6.9375); Directrix: y = 7.0625

Answer

Vertex: (3, 7); Axis of Symmetry: x = 3; Focus: (3, 7.0625); Directrix: y = 6.9375

Answer

Vertex: (3, -7); Axis of Symmetry: x = 3; Focus: (3, -6.9375); Directrix: y = -7.0625

Question 6

For the quadratic function

y = 2(x - 3)^2 + 4

, determine the vertex, axis of symmetry, focus, and directrix.

Accepted Answer

Vertex: (5, 2); Axis of Symmetry: x = 5; Focus: (5, 2.0833); Directrix: y = 1.9167

Answer

Vertex: (-5, 2); Axis of Symmetry: x = -5; Focus: (-5, 2.0833); Directrix: y = 1.9167

Answer

Vertex: (5, 2); Axis of Symmetry: y = 5; Focus: (5, 1.9167); Directrix: y = 2.0833

Answer

Vertex: (5, -2); Axis of Symmetry: x = 5; Focus: (5, -1.9167); Directrix: y = -2.0833

Question 7

Given the equation

y = 2(x - 3)^2 + 4

, what are the vertex, axis of symmetry, focus, and directrix?

Accepted Answer

Vertex: (2, 8); Axis of Symmetry: x = 2; Focus: (2, 7.875); Directrix: y = 8.125

Answer

Vertex: (2, -8); Axis of Symmetry: y = 2; Focus: (2, -8.125); Directrix: y = -7.875

Answer

Vertex: (2, 8); Axis of Symmetry: x = 8; Focus: (2, 8.125); Directrix: y = 7.875

Answer

Vertex: (-2, 8); Axis of Symmetry: x = -2; Focus: (-2, 8.125); Directrix: y = 7.875

Question 8

For the parabola represented by

y = 2(x - 3)^2 + 4

, find the vertex, axis of symmetry, focus, and directrix.

Accepted Answer

Vertex: (-1, 4); Axis of Symmetry: x = -1; Focus: (-1, 4.125); Directrix: y = 3.875

Answer

Vertex: (-1, -4); Axis of Symmetry: x = -1; Focus: (-1, -3.875); Directrix: y = -4.125

Answer

Vertex: (-1, 4); Axis of Symmetry: x = 4; Focus: (-1, 4.875); Directrix: y = 3.125

Answer

Vertex: (1, 4); Axis of Symmetry: x = 1; Focus: (1, 4.125); Directrix: y = 3.875

Question 9

Determine the vertex, axis of symmetry, focus, and directrix for the parabola described by the equation

y = 2(x - 3)^2 + 4

.

Accepted Answer

Vertex: (-3, 1); Axis of Symmetry: x = -3; Focus: (-3, 0.9167); Directrix: y = 1.0833

Answer

Vertex: (3, 1); Axis of Symmetry: x = 3; Focus: (3, 1.0833); Directrix: y = 0.9167

Answer

Vertex: (-3, 1); Axis of Symmetry: y = -3; Focus: (-3, 1.0833); Directrix: y = 0.9167

Answer

Vertex: (-3, -1); Axis of Symmetry: x = -3; Focus: (-3, -1.0833); Directrix: y = -0.9167

Question 10

For the quadratic equation

y = 2(x - 3)^2 + 4

, identify the vertex, axis of symmetry, focus, and directrix.

Accepted Answer

Vertex: (7, -4); Axis of Symmetry: x = 7; Focus: (7, -3.95); Directrix: y = -4.05

Answer

Vertex: (-7, -4); Axis of Symmetry: x = 7; Focus: (-7, -3.95); Directrix: y = -4.05

Answer

Vertex: (7, 4); Axis of Symmetry: x = -7; Focus: (7, 4.05); Directrix: y = 3.95

Answer

Vertex: (7, -4); Axis of Symmetry: y = 7; Focus: (7, -4.05); Directrix: y = -3.95

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