Graphing ParabolasGraphing ParabolasMPM 2D1

AgendaAgendaWarm upProperties of ParabolasParabolas in our LivesPractical ApplicationsTOC

Warm upWarm upClass Websitehttp://mcgregormpm2d1.wikispac

es.com/

Untie the knot

Properties of ParabolasProperties of Parabolas

Matching ActivityMatching ActivityYou will be given a word, or a

property of the parabola shownYou are responsible for finding

the person with the paper that is the match to yours

Sit with your partner when you found them

Matching ActivityMatching Activity

(-2, -7)

(0, 0.64)

a = 1

Graph to EquationGraph to Equation

(1, -2)

(2, -1)

Graph to EquationGraph to Equationh = 1, k = -2x = 2, y = -1y = a(x-h)2+k-1 = a(2-1)2-2-1 + 2 = a(1) 2

1 = aEquation

◦y = (x-1) 2-2

Parabolas in our LivesParabolas in our LivesTop edge of a spoonMotion of a swingFace shapeRoller coasterArrow projectoryA bowArch of a bridgeHorseshoeTop of a mushroomShoe front

Practical ApplicationsPractical ApplicationsThe flight path of a firework is

modelled by the relation h = -5(t-5)2 + 127, where h is the height, in metres, of the firework above the ground and t is the time, in seconds, since the firework was fired.

Practical ApplicationsPractical ApplicationsA) what is the maximum height

reached by the firework? How many seconds after it was fired does the firework reach this height?

Looking for the vertex point◦ Maximum height y coordinate (k)◦ Seconds after fired x coordinate (h)

k = 127h = 5

Practical ApplicationsPractical ApplicationsB) How high was the firework above

the ground when it was fired?Looking for the y-intercept (firework

was fired at t=0)Sub in t=0h = -5(0-5)2 + 127h = -5(-5)2 + 127h = -5(25)+127h = -125+127h = 2 m

TOCTOCState the vertex and axis of

symmetry for the following equation:

y = (x+2)2 + 4

Homework◦Handout◦Pg. 185, Q # 6, 8, 13