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Parabola y=x2+24 didilatasi [P(a,b), D(k)] di bawah ini. Tentukan persamaan bayangan parabola tersebut dan tentukan pula puncak dari bayangan parabolanya. b. a=2, b=−1, dan k=21​

Pertanyaan

Parabola begin mathsize 14px style y equals x squared plus 24 end style didilatasi open square brackets straight P open parentheses a comma b close parentheses comma space straight D open parentheses k close parentheses close square brackets di bawah ini. Tentukan persamaan bayangan parabola tersebut dan tentukan pula puncak dari bayangan parabolanya.

b. a equals 2 comma space b equals negative 1 comma space dan space k equals 1 half 

O. Rahmawati

Master Teacher

Mahasiswa/Alumni UIN Sunan Gunung Djati Bandung

Jawaban terverifikasi

Jawaban

titik puncak persamaan bayangan parabola tersebut adalah open parentheses 0 comma space minus 23 over 2 close parentheses.

Pembahasan

Suatu titik didilatasi oleh open square brackets straight P open parentheses a comma b close parentheses comma space straight D open parentheses k close parentheses close square brackets maka bayangannya adalah:

open parentheses table row cell x apostrophe end cell row cell y apostrophe end cell end table close parentheses equals open parentheses table row k 0 row 0 k end table close parentheses open parentheses table row cell x minus a end cell row cell y minus b end cell end table close parentheses plus open parentheses table row a row b end table close parentheses

  • Menentukan persamaan bayangan parabola dengan a equals 2 comma space b equals negative 1 comma space dan space k equals 1 half.

open parentheses table row cell x apostrophe end cell row cell y apostrophe end cell end table close parentheses equals open parentheses table row cell 1 half end cell 0 row 0 cell 1 half end cell end table close parentheses open parentheses table row cell x minus 2 end cell row cell y minus left parenthesis negative 1 right parenthesis end cell end table close parentheses plus open parentheses table row 2 row cell negative 1 end cell end table close parentheses open parentheses table row cell x apostrophe end cell row cell y apostrophe end cell end table close parentheses equals open parentheses table row cell 1 half x minus 2 end cell row cell 1 half y plus 1 half end cell end table close parentheses plus open parentheses table row 2 row cell negative 1 end cell end table close parentheses open parentheses table row cell x apostrophe end cell row cell y apostrophe end cell end table close parentheses equals open parentheses table row cell 1 half x end cell row cell 1 half left parenthesis y minus 1 right parenthesis end cell end table close parentheses

diperoleh:

x apostrophe equals 1 half x rightwards arrow x equals 2 x apostrophe... left parenthesis 1 right parenthesis y apostrophe equals 1 half open parentheses y minus 1 close parentheses rightwards arrow y equals 2 y apostrophe plus 1... left parenthesis 2 right parenthesis

Substitusi persamaan (1) dan (2) ke persamaan parabola:

table attributes columnalign right center left columnspacing 0px end attributes row y equals cell x squared plus 24 end cell row cell 2 y apostrophe plus 1 end cell equals cell open parentheses 2 x apostrophe close parentheses squared plus 24 end cell row cell 2 y apostrophe end cell equals cell 4 open parentheses x apostrophe close parentheses squared minus 23 end cell row cell y apostrophe end cell equals cell fraction numerator 4 open parentheses x apostrophe close parentheses squared minus 23 over denominator 2 end fraction end cell row cell y apostrophe end cell equals cell 2 open parentheses x apostrophe close parentheses squared minus 23 over 2 end cell end table

  • Menentukan titik puncak dari Error converting from MathML to accessible text. dengan a equals 2 comma space b equals 0 comma space dan space c equals negative 23 over 2.

x subscript p equals negative fraction numerator b over denominator 2 a end fraction x subscript p equals negative fraction numerator 0 over denominator 2 open parentheses 2 close parentheses end fraction x subscript p equals 0

dan

table attributes columnalign right center left columnspacing 0px end attributes row blank blank y end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell blank subscript p end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator D over denominator 4 a end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank y end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell blank subscript p end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator b squared minus 4 a c over denominator 4 a end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank y end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell blank subscript p end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator open parentheses 0 close parentheses squared minus 4 open parentheses 2 close parentheses open parentheses negative begin display style 23 over 2 end style close parentheses over denominator 4 open parentheses 2 close parentheses end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank y end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell blank subscript p end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 0 plus 92 over denominator 8 end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank y end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell blank subscript p end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 92 over 8 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank y end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell blank subscript p end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 23 over 2 end cell end table

Jadi, titik puncak persamaan bayangan parabola tersebut adalah open parentheses 0 comma space minus 23 over 2 close parentheses.

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