Question 1(Multiple Choice Worth 2 points) Find the standard form of the equation of the parabola with a focus at (0, 2) and a directrix at y = -2. y2 = 2x y = one divided by twox2 y2 = 8x y = one divided by eightx2 Question 2(Multiple Choice Worth 1 points) Find the vertex, focus, directrix, and focal width of the parabola. x2 = 12y Vertex: (0, 0); Focus: (3, 0); Directrix: x = 3; Focal width: 3 Vertex: (0, 0); Focus: (0, 3); Directrix: y = -3; Focal width: 12 Vertex: (0, 0); Focus: (3, 0); Directrix: y = 3; Focal width: 48 Vertex: (0, 0); Focus: (0, -3); Directrix: x = -3; Focal width: 48 Question 3(Multiple Choice Worth 1 points) Find the standard form of the equation of the parabola with a vertex at the origin and a focus at (0, -4). y = negative one divided by fourx2 y2 = -4x y2 = -16x y = negative one divided by sixteenx2 Question 4(Multiple Choice Worth 2 points) Find the vertex, focus, directrix, and focal width of the parabola. x = 4y2 Vertex: (0, 0); Focus: one divided by four comma zero; Directrix: x = negative one divided by four; Focal width: 0.25 Vertex: (0, 0); Focus: one divided by sixteen comma zero; Directrix: x = one divided by sixteen; Focal width: 16 Vertex: (0, 0); Focus: zero comma one divided by sixteen; Directrix: y = negative one divided by sixteen; Focal width: 16 Vertex: (0, 0); Focus: one divided by sixteen comma zero; Directrix: x = negative one divided by sixteen; Focal width: 0.25 Question 5(Multiple Choice Worth 2 points) Find the standard form of the equation of the parabola with a focus at (-4, 0) and a directrix at x = 4. y2 = -8x 16y = x2 y = negative one divided by sixteenx2 x = negative one divided by sixteeny2 Question 6 (Essay Worth 2 points) A building has an entry the shape of a parabolic arch 96 ft high and 18 ft wide at the base, as shown below. A parabola opening down with vertex at the origin is graphed on the coordinate plane. The height of the parabola from top to bottom is ninety six feet and its width from left to right is eighteen feet. Find an equation for the parabola if the vertex is put at the origin of the coordinate system.
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