Find an Equation in Standard Form of the Parabola Passing Through the Points

Name

Class

Date

Modeling with Quadratic Functions

4-3

Practice

Form G

Find an equation in standard form of the parabola passing through the points.

1. (1, 1), (2, 5), (3, 7)2. (1, 4), (2, 3), (3, 4)

3. (2, 8), (3, 8), (6, 4)4. (1, 12), (2, 6), (4, 12)

5. (1, 12), (0, 6), (3, 0)6. (2, 4), (1, 1), (3, 11)

7. (1, 6), (0, 0), (2, 6)8. (3, 2), (1, 6), (4, 9)

9. 10.

11. 12.

13.The table shows the number n of tickets to a school play
sold t days after the tickets went on sale, for several days.

a.Findaquadraticmodelforthedata.

b.Usethemodeltofindthenumberofticketssoldonday7.

c.Whenwasthegreatestnumberofticketssold?

14.Thetablegivesthenumberofpairsofskissoldinasportinggoods store for several months last year.

a.Findaquadraticmodelforthedata,usingJanuary as month 1, February as month 2, andso on.

b.Usethemodeltopredictthenumberofpairsofskissoldin November.

c.Inwhatmonthwerethefewestskissold?

Prentice Hall Gold Algebra 2 • Teaching Resources

Name

Class

Date

Modeling with Quadratic Functions

4-3

Practice (continued)

Form G

Determine whether a quadratic model exists for each set of values. If so, write the model.

15. f(1) =7, f(1) = 1, f(3) = 116. f(1) = 13, f(0) = 6, f(2) =8

17. f(2) = 2, f(4) =1, f(2) = 018. f(2) = 6, f(0) =4, f(2) =6

19.a.Complete the table. It shows the sum of the counting numbers from 1 through n.

b.Writeaquadraticmodelforthedata.

c. Predictthesumofthefirst50countingnumbers.

20.Onasuspensionbridge,theroadwayishungfromcableshangingbetweensupport towers. The cable of one bridge is in the shape of the parabolay = 0.1x27x + 150, where y is the height in feet of the cable above theroadway at the distance x feet from a support tower.

a.Whatistheclosestthecablecomestotheroadway?

b.Howfarfromthesupporttowerdoesthisoccur?

21.The owner of a small motel has an unusual idea to increase revenue. The motel has 20 rooms. He advertises that each night will cost a baserate of $48 plus $8 times the number of empty rooms that night. Forexample, if all rooms are occupied, he will have a total income of 20 $48 = $960. But, if three rooms are empty, then his total incomewill be (20 –3) ($48 + $8 ·3) = 17 $72 = $1224.

a.Writealinearexpressiontoshowhowmanyroomsareoccupiedifnrooms are empty.

b.Writealinearexpressiontoshowthepricepaidindollarsperroomif n rooms are empty.

c.Multiplytheexpressionsfromparts(a)and(b)toobtainaquadraticmodel for the data. Write the result in standard form.

d.Whatwilltheowner’stotalincomebeif10roomsareempty?

e.Whatisthenumberofemptyroomsthatresultsinthemaximumincome for the owner?

Prentice Hall Gold Algebra 2 • Teaching Resources