tentukan fungsi kuadrat yang grafiknya melalui titik (-3,4), (0,7) dan (1,5)

<p>Jawaban yang benar :</p><p><strong>f(x) = -3/4 x² - 5/4 x + 7</strong></p><p>&nbsp;</p><p>Pembahasan :</p><p>Rumus umum fungsi kuadrat adalah</p><p><strong>f(x) = ax² + bx + c</strong></p><p>atau</p><p><strong>y = ax² + bx + c</strong></p><p>&nbsp;</p><p><strong>Melalui (-3,4) berarti x = -3 dan y = 4</strong></p><p>y = ax² + bx + c</p><p>4 = a(-3)² + (-3)b + c</p><p>4 = 9a - 3b + c &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;(1)</p><p>&nbsp;</p><p><strong>Melalui (0,7) berarti x = 0 dan y = 7</strong></p><p>y = ax² + bx + c</p><p>7 = a(0)² + (0)b + c</p><p>7 = &nbsp;c &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;(2)</p><p>&nbsp;</p><p><strong>Melalui (1,5) berarti x = 1 dan y = 5</strong></p><p>y = ax² + bx + c</p><p>5 = a(1)² + (1)b + c</p><p>5 = a &nbsp;+ b + c &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;(3)</p><p>&nbsp;</p><p><strong>Substitusikan c = 7 ke persamaan (1) dan (3)</strong></p><p>4 = 9a - 3b + c &nbsp; &nbsp;</p><p>4 = 9a - 3b + 7</p><p>4 - 7 = 9a -3b</p><p>-3 = 9a - 3b &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;(dibagi 3)</p><p>-1 = 3a - b &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; (4)</p><p>&nbsp;</p><p>5 = a &nbsp;+ b + c &nbsp;&nbsp;</p><p>5 = a + b + 7</p><p>5 - 7 = a + b</p><p>-2 = a + b &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;(5)</p><p>&nbsp;</p><p><strong>Eliminasi b dari persamaan (4) dan (5) untuk mendapat nilai a</strong></p><p>&nbsp;-1 = 3a - b&nbsp;</p><p><u>&nbsp;-2 = a + b &nbsp;</u> +</p><p>-3 = 4a</p><p>a = -3/4</p><p>&nbsp;</p><p><strong>Substitusikan a = -3/4 ke persamaan (5)</strong></p><p>-2 = a + b&nbsp;</p><p>-2 = -3/4 + b</p><p>b = -2 + 3/4</p><p>&nbsp; &nbsp; = -8/4 + 3/4</p><p>&nbsp; &nbsp; = -5/4</p><p>&nbsp;</p><p><strong>Substitusikan a = -3/4, b = -5/4 dan c = 7 ke rumus umum fungsi</strong></p><p>f(x) = ax² + bx + c</p><p><strong>f(x) = -3/4 x² - 5/4 x + 7</strong></p>