Pertanyaan

Let f ( x ) = a x 2 + b x + c , where discriminant D = b 2 − 4 a c . Show that: a. f ( 2 a − b + h ) = a h 2 − 4 a D

Let $f (x) = a x^{2} + b x + c$ , where discriminant $D = b^{2} - 4 a c$ . Show that:

a. $f (\frac{- b}{2 a} + h) = a h^{2} - \frac{D}{4 a}$

I. Sutiawan

Master Teacher

Mahasiswa/Alumni Universitas Pasundan

Jawaban terverifikasi

Jawaban

untuk dimana , berlaku

untuk

f left parenthesis x right parenthesis equals a x squared plus b x plus c

dimana

, berlaku $f open parentheses fraction numerator negative b over denominator 2 a end fraction plus h close parentheses equals a h squared minus fraction numerator D over denominator 4 a end fraction$

Pembahasan

Diketahui dan , maka: Sehingga: Jadi, untuk dimana , berlaku

Diketahui f left parenthesis x right parenthesis equals a x squared plus b x plus c dan D equals b squared minus 4 a c , maka:

$table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses negative fraction numerator b over denominator 2 a end fraction plus h close parentheses end cell equals cell a open parentheses negative fraction numerator b over denominator 2 a end fraction plus h close parentheses squared plus b open parentheses negative fraction numerator b over denominator 2 a end fraction plus h close parentheses plus c end cell row blank equals cell a open parentheses fraction numerator b squared over denominator 4 a squared end fraction minus fraction numerator b h over denominator a end fraction plus h squared close parentheses minus fraction numerator b squared over denominator 2 a end fraction plus b h plus c end cell row blank equals cell fraction numerator b squared over denominator 4 a end fraction minus up diagonal strike b h end strike plus a h squared minus fraction numerator b squared over denominator 2 a end fraction plus up diagonal strike b h end strike plus c end cell row blank equals cell a h squared plus fraction numerator b squared over denominator 4 a end fraction minus fraction numerator b squared over denominator 2 a end fraction plus c end cell row blank equals cell a h squared plus fraction numerator b squared minus 2 b squared plus 4 a c over denominator 4 a end fraction end cell row blank equals cell a h squared plus fraction numerator negative b squared plus 4 a c over denominator 4 a end fraction end cell row blank equals cell a h squared plus fraction numerator negative left parenthesis b squared minus 4 a c right parenthesis over denominator 4 a end fraction end cell row blank equals cell a h squared minus fraction numerator b squared minus 4 a c over denominator 4 a end fraction end cell row blank equals cell a h squared minus fraction numerator D over denominator 4 a end fraction end cell end table$

Sehingga:

Jadi, untuk dimana , berlaku $f open parentheses fraction numerator negative b over denominator 2 a end fraction plus h close parentheses equals a h squared minus fraction numerator D over denominator 4 a end fraction$

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