Pertanyaan

Persamaan fungsi kuadrat yang grafiknya memotong sumbu X di titik ( 2 3 , 0 ) dan ( − 3 , 0 ) serta melalui titik ( 2 , 5 ) adalah ....

$Persamaan fungsi kuadrat yang grafiknya memotong sumbu X di titik (\frac{3}{2}, 0) dan (- 3, 0) serta melalui titik (2, 5) adalah ....$

Y. Laksmi

Master Teacher

Mahasiswa/Alumni Universitas Negeri Semarang

Jawaban terverifikasi

Pembahasan

$Persamaan space fungsi space kuadrat space yang space memotong space sumbu minus straight X space di space left parenthesis straight x subscript 1 comma 0 right parenthesis space dan space left parenthesis straight x subscript 2 comma 0 right parenthesis space adalah space straight f left parenthesis straight x right parenthesis equals straight y equals straight a left parenthesis straight x minus straight x subscript 1 right parenthesis left parenthesis straight x minus straight x subscript 2 right parenthesis left parenthesis straight i right parenthesis space Maka space persamaan space fungsi space kuadrat space yang space memotong space sumbu space straight X space di space titik space open parentheses 3 over 2 comma 0 space close parentheses space dan space left parenthesis negative 3 comma 0 right parenthesis space space space space space straight y equals straight a open parentheses straight x minus 3 over 2 close parentheses left parenthesis straight x minus left parenthesis negative 3 right parenthesis right parenthesis space space space space straight y equals straight a open parentheses straight x minus 3 over 2 close parentheses left parenthesis straight x plus 3 right parenthesis left parenthesis ii right parenthesis thin space Untuk space mencari space nilai space straight a comma space substitusikan space titik space yang space dilalui space yaitu space left parenthesis 2 comma 5 right parenthesis space ke space persamaan space diatas comma space dengan space straight x equals 2 space dan space straight y equals 5 space space space space space space space 5 equals straight a open parentheses 2 minus 3 over 2 close parentheses left parenthesis 2 minus left parenthesis negative 3 right parenthesis space space space space space space space 5 equals straight a open parentheses fraction numerator 4 minus 3 over denominator 2 end fraction close parentheses left parenthesis 5 right parenthesis space space space space space space space 5 equals straight a open parentheses 1 half close parentheses left parenthesis 5 right parenthesis space space space space space space space 5 equals 5 over 2 straight a space space space space space space space straight a equals 2 left parenthesis iii right parenthesis thin space Kemudian space masukan space nilai space straight a equals 2 space ke space persamaan space straight y space equals straight a open parentheses straight x minus 3 over 2 close parentheses left parenthesis straight x plus 3 right parenthesis space space space space space space straight y equals 2 open parentheses straight x minus 3 over 2 close parentheses left parenthesis straight x plus 3 right parenthesis space space space space space space straight y equals left parenthesis 2 straight x minus 3 right parenthesis left parenthesis straight x plus 3 right parenthesis space space space space space space straight y equals 2 straight x squared plus 6 straight x minus 3 straight x minus 9 space space space space space space straight y equals 2 straight x squared plus 3 straight x minus 9$