Grafik fungsi dengan a adalah bilangan bulat posi...

Grafik fungsi $begin mathsize 14px style y equals open parentheses straight a minus 2 close parentheses x squared minus 2 straight a x plus 3 straight a end style$ dengan a adalah bilangan bulat positif, menyinggung sumbu-x di titik $begin mathsize 14px style straight P left parenthesis straight x subscript 1 comma straight y subscript 1 right parenthesis end style$ dan memotong sumbu-y di titik $begin mathsize 14px style straight Q open parentheses straight x subscript 2 comma straight y subscript 2 close parentheses end style$ . Panjang ruas garis PQ adalah ... satuan.

Jawaban:

$begin mathsize 14px style y equals open parentheses straight a minus 2 close parentheses x squared minus 2 straight a x plus 3 straight a end style$

karena grafik menyinggung sumbu x, artinya $begin mathsize 14px style straight D equals 0 end style$ .

$Error converting from MathML to accessible text.$

maka diperoleh fungsi

$begin mathsize 14px style straight y equals open parentheses 3 minus 2 close parentheses straight x squared minus 2 open parentheses 3 close parentheses straight x plus 3 open parentheses 3 close parentheses straight y equals straight x squared minus 6 straight x plus 9 end style$

Titik singgung sumbu x

$begin mathsize 14px style space space space space straight x squared minus 6 straight x plus 9 equals 0 open parentheses straight x minus 3 close parentheses open parentheses straight x minus 3 close parentheses equals 0 space space space space space space space space space space space space space space space space space space straight x equals 3 space space space space space straight P open parentheses 3 comma 0 close parentheses end style$

Titik potong sumbu y

$begin mathsize 14px style straight f open parentheses straight x close parentheses equals straight x squared minus 6 straight x plus 9 straight f open parentheses 0 close parentheses equals open parentheses 0 close parentheses squared minus 6 open parentheses 0 close parentheses plus 9 straight f open parentheses 0 close parentheses equals 9 straight Q open parentheses 0 comma 9 close parentheses end style$

Panjang ruas PQ

$begin mathsize 14px style open vertical bar PQ close vertical bar equals square root of open parentheses straight x subscript 1 minus straight x subscript 2 close parentheses squared plus open parentheses straight y subscript 1 minus straight y subscript 2 close parentheses squared end root open vertical bar PQ close vertical bar equals square root of open parentheses 3 minus 0 close parentheses squared plus open parentheses 0 minus 9 close parentheses squared end root open vertical bar PQ close vertical bar equals square root of 90 open vertical bar PQ close vertical bar equals 3 square root of 10 end style$

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