Fungsi kuadrat yang melalui titik (1,-4), (0,-3) dan (4,5) adalah

<p>Jawaban yang tepat adalah y = x² &nbsp;- 2x - 3 atau f(x) = x² - 2x - 3</p><p>&nbsp;</p><p><strong>Pembahasan :</strong></p><p>Fungsi kuadrat yang melalui titik (1,-4), (0,-3) dan (4,5)</p><p>&nbsp;</p><p>Rumus umum fungsi kuadrat :</p><p>y = ax² + bx + c</p><p>&nbsp;</p><p>Melalui (1, -4)</p><p>-4 = a(1)² + b(1) + c&nbsp;</p><p>-4 = a + b + c &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;(1)</p><p>&nbsp;</p><p>Melalui (0,-3)</p><p>-3 = c &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;(2)</p><p>&nbsp;</p><p>Melalui (4,5)</p><p>5 = a(4)² + b(4) + c</p><p>5 = 16a + 4b + c &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; (3)</p><p>&nbsp;</p><p>Eliminasi b dari persamaan (1) dan (3)</p><p>5 = 16a + 4b + c &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; ---&gt; 5 = 16a + 4b + c</p><p>-4 = a + b + c &nbsp; &nbsp; &nbsp; &nbsp; (dikali 4) &nbsp;---&gt;<u> -16 = 4a + 4b + 4c</u> _</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;21 = 12a - 3c &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;(4)</p><p>&nbsp;</p><p>Substitusikan persamaan (2) ke persamaan (4) untuk mencari nilai a</p><p>21 = 12a - 3c</p><p>21 = 12a - 3(-3)</p><p>21 = 12a + 9</p><p>12a = 21 - 9</p><p>12a = 12</p><p>a = 1</p><p>&nbsp;</p><p>Substitusikan a = 1 dan c = -3 ke persamaan (1)</p><p>-4 = a + b + c</p><p>-4 = 1 + b - 3</p><p>-4 = b - 2</p><p>b = -4 + 2</p><p>b = -2</p><p>&nbsp;</p><p>Masukkan a = 1, b = -2 dan c =-3 ke rumus umum fungsi</p><p>y = x² &nbsp;- 2x - 3 atau f(x) = x² - 2x - 3</p>