CONIC SECTIONS PARABOLA Section 10 2 Precalculus Revised

SHAPE OF A PARABOLA FROM A CONE 1/25/2022 8: 23 PM 10. 2: Parabola 2

REAL-LIFE EXAMPLES 1/25/2022 8: 23 PM 10. 2: Parabola 3

DEFINITIONS 1/25/2022 8: 23 PM 10. 2: Parabola 4

FORMULAS TO KNOW: Directrix: Axis of Symmetry: Points of Latus Rectum: 1/25/2022 8: 23 PM 10. 2: Parabola 5

FORMULAS TO KNOW: Directrix: Axis of Symmetry: Points of Latus Rectum: 1/25/2022 8: 23 PM 10. 2: Parabola 6

FORMULAS TO KNOW: All Standard Form Equations Center Length of Latus Rectum 1/25/2022 8: 23 PM 10. 2: Parabola 7

REVIEW OF PARENT FUNCTION PARABOLAS 1/25/2022 8: 23 PM 10. 2: Parabola 8

THE PARABOLA Brief Clip Where do we see the focus point used in real-life? 1/25/2022 8: 24 PM 10. 2: Parabola 9

HORIZONTAL PARABOLA Horizontal parabola due to its ‘Axis of Symmetry’ y=k (h, k) F (p, 0) x = –p 1/25/2022 8: 24 PM 10. 2: Parabola 10

VERTICAL PARABOLA (p, 0) F (h, k) y = –p x=k 1/25/2022 8: 24 PM 10. 2: Parabola Vertical parabola due to its ‘Axis of Symmetry’ 11

REVIEW OF PARENT FUNCTION PARABOLAS 1/25/2022 8: 24 PM 10. 2: Parabola 12

STEPS IN WRITING CONIC SECTIONS OF PARABOLAS 1/25/2022 8: 24 PM 10. 2: Parabola 13

EXAMPLE 1 1/25/2022 8: 24 PM 10. 2: Parabola 14

EXAMPLE 1 1/25/2022 8: 24 PM 10. 2: Parabola 15

EXAMPLE 1 1/25/2022 8: 24 PM 10. 2: Parabola 16

EXAMPLE 1 1/25/2022 8: 24 PM 10. 2: Parabola 17

EXAMPLE 1 1/25/2022 8: 24 PM 10. 2: Parabola 18

EXAMPLE 1 Vertex: P: Focus Point: F Directrix: Axis of Symmetry: Latus Rectum: 1/25/2022 8: 24 PM 10. 2: Parabola Length of LR: 19

EXAMPLE 2 Vertex: P: Focus Point: F Directrix: Axis of Symmetry: Latus Rectum: 1/25/2022 8: 24 PM 10. 2: Parabola Length of LR: 20

YOUR TURN Vertex: P: Focus Point: F Directrix: Axis of Symmetry: Latus Rectum: 1/25/2022 8: 25 PM 10. 2: Parabola Length of LR: 21

EXAMPLE 3 F P=2 1/25/2022 8: 25 PM 10. 2: Parabola 22

YOUR TURN 1/25/2022 8: 25 PM 10. 2: Parabola 23

EXAMPLE 4 Vertex: P: Focus Point: Directrix: F Axis of Symmetry: Latus Rectum: 1/25/2022 8: 25 PM 10. 2: Parabola Length of LR: 24

EXAMPLE 5 Vertex: P: Focus Point: F Directrix: Axis of Symmetry: Latus Rectum: 1/25/2022 8: 25 PM 10. 2: Parabola Length of LR: 25

YOUR TURN Vertex: P: Focus Point: F Directrix: Axis of Symmetry: Latus Rectum: 1/25/2022 8: 25 PM 10. 2: Parabola Length of LR: 26

EXAMPLE 6 F 1/25/2022 8: 26 PM 10. 2: Parabola 27

EXAMPLE 7 1/25/2022 8: 26 PM 10. 2: Parabola 28

YOUR TURN 1/25/2022 8: 26 PM 10. 2: Parabola 29

CONVERTING TO STANDARD FORM 1/25/2022 8: 26 PM 10. 2: Parabola 30

EXAMPLE 8 1/25/2022 8: 26 PM 10. 2: Parabola 31

EXAMPLE 8 1/25/2022 8: 26 PM 10. 2: Parabola 32

EXAMPLE 8 1/25/2022 8: 26 PM 10. 2: Parabola 33

EXAMPLE 9 1/25/2022 8: 26 PM 10. 2: Parabola 34

YOUR TURN 1/25/2022 8: 26 PM 10. 2: Parabola 35