1. Day 18 Warm-Up
1) Which of the following problems is a circle and which is a parabola? Why? A) 2 𝑥 2 +5𝑥+𝑦+14=0 B) 4 𝑥 2 +4 𝑦 2 −6𝑥+8𝑦−10=0 2) Identify the focus and directrix of the parabola: 3𝑥 2 =4𝑦 3) Identify the vertex of the parabola: 𝑦 2 −6𝑥−16𝑦+52=0

2. #1 Warm-Up Answer: A is a PARBOLA because it has ONE squared variable.
1) Which of the following problems is a circle and which is a parabola? Why? A) 2 𝑥 2 +5𝑥+𝑦+14=0 B) 4 𝑥 2 +4 𝑦 2 −6𝑥+8𝑦−10=0
Answer:
A is a PARBOLA because it has ONE squared variable.
B is a CIRCLE because it has TWO squared variables, their leading coefficients are the SAME NUMBER and it is ADDITION.

3. #2 Warm-Up Focus: (0, 1/3) Directrix : y = -1/3
2) Identify the focus and directrix of the parabola: 3𝑥 2 =4𝑦
Focus: (0, 1/3)
Directrix : y = -1/3

4. Answer: 𝑦−8 2 =6(𝑥+2) #3 Warm-Up Vertex: (-2, 8)
3) Identify the vertex of the parabola: 𝑦 2 −6𝑥−16𝑦+52=0
Answer:
𝑦−8 2 =6(𝑥+2)
Vertex: (-2, 8)

5. Mini Assessment ON FRIDAY
Circles: Completing the square, graphing, creating an equation, intersection of lines and circles Parabolas: completing the square, graphing, identifying the focus and the directrix

6. SWBAT Write an equation of a parabola
Day 18 – Parabolas Part 2
SWBAT Write an equation of a parabola

7. Write an equation of a parabola.
Vertex is (0, 0)
Directrix is y = -p = 1 2
Substitute for p in the standard form of the equation of a parabola.
𝑥 2 =4𝑝𝑦 → 𝑥 2 =4 − 1 2 𝑦
𝒙 𝟐 =−𝟐𝒚

8. Write the standard form of the equation of a parabola with the given:
Vertex at (0,0) and:
Directrix at x = 3
Directrix at y = -1
Directrix at y =

9. Write the standard form of the equation of a parabola with the given:
Vertex at (0,0) and:
Focus at (2, 0)
Focus at (0, 1)
Focus at (0, -6)

10. Exit Ticket
1) How can you tell when an equation is a parabola? 2) How can you tell when an equation is a circle? 3) Identify the vertex of the parabola: 𝑦 2 −6𝑥−16𝑦+52=0 4) Write an equation with Vertex at (0,0) & Directrix at x = 3. 5) Write an equation with Vertex at (0,0) & Focus at (2, 0).