Persamaan parabola maka puncak parabolanya adalah...

Persamaan parabola $begin mathsize 14px style open parentheses y minus 3 close parentheses squared equals 4 open parentheses x plus 5 close parentheses end style$ maka puncak parabolanya adalah $begin mathsize 14px style open parentheses a comma b close parentheses end style$ , maka nilai $begin mathsize 14px style a minus b equals end style$ ....

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... $undefined$

Jawaban:

Koordinat titik puncak suatu parabola $begin mathsize 14px style open parentheses x subscript p comma space y subscript p close parentheses end style$ dapat ditentukan dengan menggunakan persamaan:

Karena parabola merupakan fungsi kuadrat maka kita jabarkan terlebih dahulu persamaan yang diberikan ke dalam bentuk persamaan kuadrat:

$begin mathsize 14px style left parenthesis y minus 3 right parenthesis squared equals 4 left parenthesis x plus 5 right parenthesis y squared minus 6 y plus 9 equals 4 x plus 20 y squared minus 6 y plus 9 minus 4 x minus 20 equals 4 x y squared minus 6 y minus 11 equals 4 x x equals open parentheses 1 fourth close parentheses y squared minus open parentheses 6 over 4 close parentheses y minus 11 over 4 end style$

Maka nilai

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row a equals cell 1 fourth end cell row b equals cell negative 6 over 4 equals negative 3 over 2 end cell row c equals cell negative 11 over 4 end cell end table end style$

Menghitung koordinat titik puncak $undefined$

Titik $begin mathsize 14px style x subscript p end style$

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell x subscript p end cell equals cell fraction numerator negative b over denominator 2 a end fraction end cell row blank equals cell fraction numerator negative open parentheses begin display style fraction numerator negative 3 over denominator 2 end fraction end style close parentheses over denominator 2 open parentheses begin display style 1 fourth end style close parentheses end fraction end cell row blank equals cell 3 over 2 cross times 2 end cell row cell x subscript p end cell equals 3 end table end style$

Titik $begin mathsize 14px style y subscript p end style$

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell y subscript p end cell equals cell fraction numerator negative open parentheses b squared minus 4 a c close parentheses over denominator 4 a end fraction end cell row cell y subscript p end cell equals cell fraction numerator negative open parentheses open parentheses begin display style fraction numerator negative 3 over denominator 2 end fraction end style close parentheses squared minus 4 open parentheses begin display style 1 fourth end style close parentheses open parentheses begin display style fraction numerator negative 11 over denominator 4 end fraction end style close parentheses close parentheses over denominator 4 open parentheses begin display style 1 fourth end style close parentheses end fraction end cell row cell y subscript p end cell equals cell fraction numerator negative open parentheses open parentheses begin display style 9 over 4 end style close parentheses plus begin display style 11 over 4 end style close parentheses over denominator 1 end fraction end cell row cell y subscript p end cell equals cell 2 over 4 end cell row cell y subscript p end cell equals cell 1 half end cell end table end style$

puncak parabolanya $begin mathsize 14px style open parentheses 3 comma space 1 half close parentheses end style$

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row a equals 3 row b equals cell 1 half end cell end table end style$

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell a minus b end cell equals cell 3 minus 1 half end cell row cell a minus b end cell equals cell 5 over 2 end cell end table end style$

Dengan demikian nilai dari $begin mathsize 14px style a minus b end style$ adalah $begin mathsize 14px style 5 over 2 end style$ .

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