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Unit 3 '- Quadratric Functions - Im3 Lesson 3: Working With Quadratic Models In Vertex Form Worksheet Page 2

IM3 -‐ L esson 3 : W orking w ith Q uadratic M odels I n V ertex F orm Unit 3 – Q uadratric F

unctions

Modeling w ith Q uadratic F unctions ( Context)

Mr S ’s s ister i s a m otorcycle i nstructor a nd r uns a t raining s chool. B ecause s he w orks f or h erself, s he c an c harge a ny

amount ( as a n h ourly c harge) t hat s he w ishes. S he k eeps t rack o f h er h ourly f ees a nd h er p rofits a nd h as p repared a

graph s howing t he r elationship b etween h er h ourly w ages a nd h er p rofits.

In t his r elation, t he v ariables:

X r epresents t he h ourly f ee m y s ister

charges

Y r epresents t he m onthly p rofit s he

makes

(a) S tate a r easonable d omain a nd r ange f or t his

(b) S tate t he c oordinates o f t he v ertex a nd e xplain i ts

relationship, g iven t he c ontext o f t he p roblem

meaning i n t his c ontext.

(e) E valuate P (45) a nd e xplain i ts m eaning.

in t his c ontext.

(d) H ENCE, w rite t he e quation i n F ACTORED f orm.

(f) E valuate P (15) a nd e xplain y our t hinking.

(g) D etermine t he e quation f or t his r elation i n V ERTEX

(h) M y s ister w ould l ike t o k now w hat h ourly f ee

form. S how y our w ork

OPTIMIZES h er p rofits?

Unit 3 '- Quadratric Functions - Im3 Lesson 3: Working With Quadratic Models In Vertex Form Worksheet Page 2