Parabolic Equations

What is a Parabola?

• The graph of a quadratic function
• The graph of a linear function
• The graph of an absolute value function
• A boat

A parabola has a vertex at (-3,2). Where is the axis of symmetry?

• y = -2
• x = 3
• x = -3
• y = 2

The vertex is sometimes halfway between the focus and directrix.

• true
• false

A parabola is the set of all points equidistant from the focus and the directrix.

• true
• false

Find the vertex, focus, and directrix of the parabola: x² = 28y

• Vertex: (0, 0) Focus: (0,7) Directrix: y=-7
• Vertex: (0, 0) Focus: (7,0) Directrix: y=7
• Vertex: (0, 0) Focus: (0,-7) Directrix: x=-7
• Vertex: (0, 0) Focus: (7, 0) Directrix: x=7

Find the standard form of the equation of the parabola whose focus (0, 4) and a directrix y=-4.

• y = (1/16)x²
• y² = 4x
• y² = 16x
• y = (1/4)x²

Find the vertex, focus, and directrix of the parabola: -(1/40)x² = y

• Vertex: (0, 0) Focus: (-20,0) Directrix: x = 10
• Vertex: (0, 0) Focus: (0,10) Directrix: y=10
• Vertex: (0, 0) Focus: (0,10) Directrix: y=-10
• Vertex: (0, 0) Focus: (0, -10) Directrix: y = 10

Which equation below represents a parabola that opens upward with a vertex at (0, -5)?

• y = x² + 5
• y = x² - 5
• y = (x - 5)²
• y = (x + 5)²

Use the distance formula to write the equation in standard form given the focus is (0,3) and the directrix is at y=5.

• x² = -4(y-3)
• (y-3) = (1/8)x²
• -4(y-4) = x²
• -(1/8)x² = (y-4)

The vertex is sometimes halfway between the focus and directrix.

• true
• false