Pertanyaan

Let g ( x ) = x 2 + 2 ( a + b ) x + 2 ( a 2 + b 2 ) ,where and b are constants. a. Show that the coordinates of the vertex is ( − ( a + b ) , ( a − b ) 2 ) (-(a + b), (a - b)2)

Let $g (x) = x^{2} + 2 (a + b) x + 2 (a^{2} + b^{2})$ ,where $a$ and $b$ are constants.

a. Show that the coordinates of the vertex is $(- (a + b), (a - b)^{2})$ (-(a + b), (a - b)2)

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Klaim

I. Sutiawan

Master Teacher

Mahasiswa/Alumni Universitas Pasundan

Jawaban terverifikasi

Jawaban

titik puncak dari fungsi kuadrat adalah .

titik puncak dari fungsi kuadrat g open parentheses x close parentheses equals x squared plus 2 open parentheses a plus b close parentheses x plus 2 open parentheses a squared plus b squared close parentheses

g open parentheses x close parentheses equals x squared plus 2 open parentheses a plus b close parentheses x plus 2 open parentheses a squared plus b squared close parentheses

adalah

left parenthesis negative left parenthesis a plus b right parenthesis comma space left parenthesis a minus b right parenthesis squared right parenthesis

Pembahasan

Diketahui , maka untuk menentukan vertex atau titik puncaknya kita dapat menggunakan rumus , sehingga: Jadi, titik puncak dari fungsi kuadrat adalah .

Diketahui g open parentheses x close parentheses equals x squared plus 2 open parentheses a plus b close parentheses x plus 2 open parentheses a squared plus b squared close parentheses , maka untuk menentukan vertex atau titik puncaknya kita dapat menggunakan rumus $left parenthesis x subscript p comma space y subscript p right parenthesis equals open parentheses negative fraction numerator b over denominator 2 a end fraction comma space minus fraction numerator D over denominator 4 a end fraction close parentheses$ , sehingga:

$table attributes columnalign right center left columnspacing 0px end attributes row cell x subscript p end cell equals cell negative fraction numerator b over denominator 2 a end fraction end cell row blank equals cell negative fraction numerator 2 left parenthesis a plus b right parenthesis over denominator 2 left parenthesis 1 right parenthesis end fraction end cell row blank equals cell negative fraction numerator 2 left parenthesis a plus b right parenthesis over denominator 2 end fraction end cell row blank equals cell negative left parenthesis a plus b right parenthesis end cell row blank blank blank row cell y subscript p end cell equals cell negative fraction numerator D over denominator 4 a end fraction end cell row blank equals cell negative fraction numerator b squared minus 4 a c over denominator 4 a end fraction end cell row blank equals cell negative fraction numerator left parenthesis 2 left parenthesis a plus b right parenthesis right parenthesis squared minus 4 left parenthesis 1 right parenthesis left parenthesis 2 left parenthesis a squared plus b squared right parenthesis right parenthesis over denominator 4 left parenthesis 1 right parenthesis end fraction end cell row blank equals cell negative fraction numerator 4 left parenthesis a squared plus 2 a b plus b squared right parenthesis minus 8 a squared minus 8 b squared over denominator 4 end fraction end cell row blank equals cell negative fraction numerator 4 a squared plus 8 a b plus 4 b squared minus 8 a squared minus 8 b squared over denominator 4 end fraction end cell row blank equals cell negative fraction numerator negative 4 a squared plus 8 a b minus 4 b squared over denominator 4 end fraction end cell row blank equals cell negative fraction numerator up diagonal strike 4 left parenthesis negative a squared plus 2 a b minus b squared right parenthesis over denominator up diagonal strike 4 end fraction end cell row blank equals cell a squared minus 2 a b plus b squared end cell row blank equals cell left parenthesis a minus b right parenthesis squared end cell end table$

Jadi, titik puncak dari fungsi kuadrat adalah .