SECONDARY MATH II // MODULE 3

SOLVING QUADRATICS & OTHER EQUATIONS – 3.8

Mathematics Vision Project

Licensed under the Creative Commons Attribution CC BY 4.0

mathematicsvisionproject.org

3.8

Needhelp?Visitwww.rsgsupport.org

READY Topic:SimplifyingRadicalsSimplifyeachoftheradicalsbelow.

1. 8 2. 18 3. 32

4. 20 5. 45 6. 80

7.Whatistheconnectionbetweentheradicalsabove?Explain.

SET Topic:Determinethenatureofthex-interceptsforeachquadraticbelow.

Giventhequadraticfunction,itsgraphorotherinformation,belowdeterminethenatureofthex-intercepts(whattypeofnumberitis).Explainorshowhowyouknow.

(Wholenumbers“𝕎”,Integers“ℤ”,Rational“ℚ”,Irrational“ℚ”,orfinally,“notReal”)

8.Determinethenatureofthex-intercepts.

9.Determinethenatureofthex-intercepts

READY, SET, GO! Name PeriodDate

SECONDARY MATH II // MODULE 3

SOLVING QUADRATICS & OTHER EQUATIONS – 3.8

Mathematics Vision Project

Licensed under the Creative Commons Attribution CC BY 4.0

mathematicsvisionproject.org

3.8

Needhelp?Visitwww.rsgsupport.org

10.Determinethenatureofthex-intercepts. 11.Determinethenatureofthex-intercepts.𝑓(𝑥) = 𝑥! + 4𝑥 – 24

𝑔(𝑥) = (2𝑥 – 1)(5𝑥 + 2)

12.Determinethenatureofthex-intercepts. 13.Determinethenatureofthex-intercepts.

𝑓(𝑥) = 2𝑥! + 3𝑥 – 5

14.Determinethenatureofthex-intercepts. 15.Determinethenatureofthex-intercepts.𝑟(𝑡) = 𝑡! − 8𝑡 + 16

ℎ(𝑥) = 3𝑥!– 5𝑥 + 9

Determinethenumberofrootsthateachpolynomialwillhave.

16.𝑥! + 7𝑥!– 𝑥! + 4𝑥 – 21 17.4𝑥! + 2𝑥! – 3𝑥 – 9 18.2𝑥! + 4𝑥! − 5𝑥! + 16𝑥 + 3

GO Topic:Findingx-interceptsforquadraticsusingfactoringandquadraticformula.Ifthegivenquadraticfunctioncanbefactoredthenfactorandprovidethex-intercepts.Ifyoucannotfactorthefunctionthenusethequadraticformulatofindthex-intercepts.

19.𝐴(𝑥) = 𝑥! + 4𝑥 – 21 20.𝐵(𝑥) = 5𝑥! + 16𝑥 + 3 21.𝐶(𝑥) = 𝑥! – 4𝑥 + 1

22.𝐷(𝑥) = 𝑥! – 16𝑥 + 4 23.𝐸(𝑥) = 𝑥! + 3𝑥 – 40 24.𝐹(𝑥) = 2𝑥! – 3𝑥 – 9

25.𝐺(𝑥) = 𝑥! – 3𝑥 26.𝐻(𝑥) = 𝑥! + 6𝑥 + 8 27.𝐾(𝑥) = 3𝑥! – 11