Parabolas

Question 1

Definition of Parabola

Answer 1

The set of all points that are equidistant from a focus F as they are from a fixed line D

Question 2

What is does the blue line represent?

Answer 2

Axis of symmetry

Question 3

Axis of Symmetry: Definition

Answer 3

Line of symmetry for a parabola that passes through the focus, vertex, and is perpendicular to directrix

Question 4

What does the blue dot represent?

Answer 4

Vertex

Question 5

Vertex: Definition

Answer 5

Point of intersection of parabola with axis of symmetry

Question 6

What does the blue line represent?

Answer 6

Directrix

Question 7

What does the blue point represent?

Answer 7

Focus

Question 8

What is focal length?

Answer 8

The distance from the focus to the vertex

Question 9

How is focal length, c, calculated for a parabola?

Answer 9

c = 1 / 4a when the “a” value is a coefficient of the QUADRATIC term

or…

c = 1/4 of coefficient multiplied to the linear factor. In other words, it is 1/4 of the FOCAL WIDTH

Question 10

What is the blue line segment?

Answer 10

Focal width

Question 11

Relationship between focal width and focal length

Answer 11

Focal width is FOUR times longer than focal length.

Question 12

y^2 = 12x

What direction does parabola open?

Answer 12

Right

Question 13

y^2 = 12x

What is the focal length?

Answer 13

3. The 12 represents the focal width. 1/4 * 12 = 3

Question 14

y^2 = 12x
What is the focal width

Answer 14

12. It is the coefficient that is multiplied to the LINEAR term

Question 15

y^2 = 12x

What is the equation of the directrix?

Answer 15

x=-3 because the focal length is three, so you go 3 units behind the vertex and graph the vertical line at that point.

Question 16

(y-3)^2 = -8(x+2)
Vertex? Focal Length? Focal Width?

Answer 16

V: (-2, 3)
FL: 2
FW: 8

Question 17

Standard form for upright parabola

Answer 17

(x-h)^2 = 4c(y-k)

or…

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

Question 18

Standard form for sideways parabola

Answer 18

(y-k)^2 = 4c(x-h)

or…

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

Question 19

Convert to Standard Form

y^2 - 2y = 8x - 1

Answer 19

STEP 1: y^2 - 2y = 8x - 1
STEP 2: y^2 - 2y + 1 = 8x -1 + 1
STEP 3: (y-1)^2 = 8x

Question 20

Convert to Standard Form: y = -1/28x^2 + 9/14x - 249/28

Answer 20

• STEP 1: y = -1/28x^2 + 9/14x - 249/28
• STEP 2: -28y = x^2 - 18x + 249
• STEP 3: -28y = x^2 - 18x + 81 + 249 - 81
• STEP 4: - 28y = (x-9)^2 + 168
• STEP 5: y = -1/28(x-9)^2 - 6 (THIS CAN BE FINAL FORM, BUT BETTER YET….)
• STEP 6: (y+6) = -1/28(x-9)^2
• STEP 7: -28(y+6) = (x-9)^2