Parabolas

Question 1

A Parabola has…

Answer 1

A Focus, A Directrix, ONE Vertex

Question 2

What is d?

Answer 2

D is the distance from the Vertex to the Focus, which equals the distance from the Vertex to the Directrix
-The Vertex is equidistant from the Focus and Directrix

Question 3

Horizontal Directrix

Answer 3

y = a number (Horizontal lines can only move along the Y-axis)

Question 4

Vertical Directrix

Answer 4

x = a number (Vertical lines can only move along the X-axis)

Question 5

What is a?

Answer 5

A = 1/4d (d=distance from vertex to focus and vertex to directrix)

Question 6

Standard Form of the Equation of a Vertical Parabola with a positive a and at (0,0)

Answer 6

y=ax^2 (opens UP!)

Question 7

Standard Form of the Equation of a Vertical Parabola with a negative a and at (0,0)

Answer 7

y=-ax^2 (opens DOWN!)

Question 8

Standard Form of the Equation of a Horizontal Parabola with a positive a and at (0,0)

Answer 8

x=ay^2 (opens RIGHT!)

Question 9

Standard Form of the Equation of a Horizontal Parabola with a negative a and at (0,0)

Answer 9

x=-ay^2 (opens LEFT!)

Question 10

Standard Form of the Equation of a Vertical Parabola with a positive a and at (h,k)

Answer 10

y=a(x-h)^2+k (opens UP!)

Question 11

Standard Form of the Equation of a Vertical Parabola with a negative a and at (h,k)

Answer 11

y=-a(x-h)^2+k (opens DOWN!)

Question 12

Standard Form of the Equation of a Horizontal Parabola with a positive a and at (h,k)

Answer 12

x=a(y-k)^2+h (opens LEFT!)

Question 13

Standard Form of the Equation of a Horizontal Parabola with a negative a and at (h,k)

Answer 13

x=-a(y-k)^2+h (opens RIGHT!)

Question 14

Horizontal vs. Vertical?

Answer 14

1. If the equation begins with y =, then the Parabola opens either up or down (along the y-axis)
   
   • positive a = up, negative a = down
2. If the Equation begins with x =, then the Parabola opens either left or right (along the x-axis)
   
   • positive a = right, negative a = left
3. If a is positive, the Parabola opens either up or right
4. If a is negative, the Parabola opens either down or left
5. Horizontal directrix = Vertical Parabola
   
   • Axis of Symmetry is perpendicular to the Directrix
6. Vertical directricx = Horizontal Parabola
   
   • Axis of Symmetry is perpendicular to the Directrix

Question 15

General Form of a Vertical Parabola (a is positive)

Answer 15

y = ax^2+bx+c

Question 16

General Form of a Horizontal Parabola (a is negative)

Answer 16

x = ay^2+by+c

Question 17

Identifying a Parabola from its General Form Equation

Answer 17

Parabolas only have 1 squared term (either #x^2 or #y^2)