fungsi kuadrat yang melalui titik A (0, -10), b (1, -6), dan c (3, 8) adalah ...

<p>Jawaban yang tepat adalah <strong>f(x) = x² + 3x - 10</strong></p><p>&nbsp;</p><p>Pembahasan :</p><p>Rumus umum fungsi kuadrat :</p><p><strong>f(x) = ax² + bx + c</strong></p><p>Melalui titik A(0,-10)</p><p>f(x) = ax² + bx + c</p><p>-10 = c &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;(1)</p><p>&nbsp;</p><p>Melalui titik B(1,-6)</p><p>f(x) = ax² + bx + c</p><p>-6 = a + b + c ; karena c = -10</p><p>-6 = a + b - 10</p><p>-6 + 10 = a + b</p><p>4 = a + b &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp;</p><p>a = 4 - b &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;(2)</p><p>&nbsp;</p><p>Melalui titik C(3,8)</p><p>f(x) = ax² + bx + c</p><p>8 = 9a + 3b + c, karena c = -10</p><p>8 = 9a + 3b - 10</p><p>8 + 10 = 9a + 3b</p><p>18 = 9a + 3b &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; (3)</p><p>&nbsp;</p><p>Substitusikan persamaan (2) ke persamaan (3)</p><p>18 = 9a + 3b&nbsp;</p><p>18 = 9(4 - b) + 3b&nbsp;</p><p>18 = 36 - 9b + 3b</p><p>18 - 36 = -6b</p><p>-18 = -6b</p><p>b = 3</p><p>&nbsp;</p><p>Substitusikan b = 3 ke persamaan (2)</p><p>a = 4 - b</p><p>&nbsp; &nbsp; = 4 - 3</p><p>&nbsp; &nbsp; = 1</p><p>&nbsp;</p><p>Menentukan rumus fungsi</p><p>Substitusikan a = 1, b = 3 dan c = -10 ke rumus umum fungsi.</p><p>f(x) = ax² + bx + c</p><p><strong>f(x) = x² + 3x - 10</strong></p>