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

#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.

#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

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)

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

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

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

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 = - 1 2

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)

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).