{"id":230091,"date":"2022-11-16T11:14:00","date_gmt":"2022-11-16T04:14:00","guid":{"rendered":"https:\/\/www.quipper.com\/id\/blog\/?p=230091"},"modified":"2023-02-06T10:21:39","modified_gmt":"2023-02-06T03:21:39","slug":"contoh-soal-fungsi-kuadrat","status":"publish","type":"post","link":"https:\/\/quipperhome.wpcomstaging.com\/mapel\/matematika\/contoh-soal-fungsi-kuadrat\/","title":{"rendered":"Contoh Soal Fungsi Kuadrat Lengkap dengan Pembahasan"},"content":{"rendered":"\n
\"Contoh<\/figure>\n\n\n\n

Hai Quipperian, tahukah kamu kedudukan fungsi di dalam Matematika itu sama seperti kedudukan garam di dalam masakan. Hampir setiap permasalahan di dalam Matematika melibatkan fungsi di dalamnya. Fungsi yang umum kamu kenal adalah fungsi kuadrat. Apakah kamu masih ingat apa itu fungsi kuadrat? Seperti apa pula cara menyelesaikan soal-soal terkait fungsi tersebut? Daripada penasaran, yuk simak selengkapnya!<\/p>\n\n\n\n

Pengertian Fungsi Kuadrat<\/strong><\/h2>\n\n\n\n

Fungsi kuadrat adalah suatu fungsi yang variabelnya memiliki pangkat tertinggi dua. Contoh fungsi kuadrat adalah f<\/em>(x<\/em>) = x<\/em>2<\/sup> + 2x<\/em> + 2. Di artikel sebelumnya, Quipper Blog sudah pernah membahas lebih lengkap tentang sifat-sifat fungsi kuadrat, bentuk grafik, serta cara pembentukannya.<\/p>\n\n\n\n

Setelah membaca artikel di atas, yuk latihan contoh soal bersama-sama.<\/p>\n\n\n\n

Contoh Soal Fungsi Kuadrat<\/strong><\/h2>\n\n\n\n

Berikut ini 10 contoh soal tentang fungsi kuadrat yang bisa kamu jadikan referensi belajar.<\/p>\n\n\n\n

Contoh soal 1<\/strong><\/h3>\n\n\n\n

Diketahui fungsi kuadrat seperti berikut.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Jika nilai x<\/em> = -1, nilai fungsi tersebut adalah \u2026.<\/p>\n\n\n\n

    \n
  1. -7<\/li>\n\n\n\n
  2. 7<\/li>\n\n\n\n
  3. 4<\/li>\n\n\n\n
  4. -4<\/li>\n<\/ol>\n\n\n\n

    Pembahasan:<\/p>\n\n\n\n

    Untuk mencari nilai fungsi, kamu hanya perlu mensubstitusikan nilai x<\/em> = -1 ke pada persamaan fungsinya seperti berikut.<\/p>\n\n\n\n

    \"\"<\/figure>\n\n\n\n

    Jadi, nilai fungsi tersebut untuk x<\/em> = -1 adalah 7.<\/p>\n\n\n\n

    Jawaban: B<\/p>\n\n\n\n

    Contoh soal 2<\/strong><\/h3>\n\n\n\n

    Diketahui grafik fungsi kuadrat <\/sub>menghasilkan grafik yang titik puncaknya berada di koordinat (16, 8) dan memotong sumbu-x positif di dua titik yang berbeda. Pernyataan yang benar adalah \u2026.<\/p>\n\n\n\n

      \n
    1. p<\/em> > 0, q<\/em> > 0, dan D > <\/em>0<\/li>\n\n\n\n
    2. p<\/em> < 0, q<\/em> < 0, dan D > <\/em>0<\/li>\n\n\n\n
    3. p<\/em> < 0, q<\/em> > 0, dan D < <\/em>0<\/li>\n\n\n\n
    4. p<\/em> < 0, q<\/em> > 0, dan D > <\/em>0<\/li>\n<\/ol>\n\n\n\n

      Pembahasan:<\/p>\n\n\n\n

      Jika grafik fungsi pada soal yang bertitik puncak (16, 8) memotong dua titik yang berbeda di sumbu-x, artinya grafik tersebut terbuka ke bawah. Sumbu simterinya berada di kanan sumbu-y. Oleh sebab itu, bisa disimpulkan bahwa p<\/em> < 0 dan q <\/em>berlainan tanda dengan p<\/em>, yaitu q<\/em> > 0. Untuk lebih jelasnya, perhatikan persamaan berikut.<\/p>\n\n\n\n

      \"\"<\/figure>\n\n\n\n

      Oleh karena grafik memotong sumbu-x positif di dua titik yang berbeda, maka dapat disimpulkan bahwa D<\/em> > 0.<\/p>\n\n\n\n

      Jadi, pernyataan yang benar adalah p<\/em> < 0, q<\/em> > 0, dan D > <\/em>0.<\/p>\n\n\n\n

      Jawaban: D<\/p>\n\n\n\n

      Contoh soal 3<\/strong><\/h3>\n\n\n\n

      Diketahui <\/sub>memiliki fungsi maksimum 16. Nilai konstanta c<\/em> adalah \u2026.<\/p>\n\n\n\n

        \n
      1. 12<\/li>\n\n\n\n
      2. -8<\/li>\n\n\n\n
      3. -10<\/li>\n\n\n\n
      4. 8<\/li>\n<\/ol>\n\n\n\n

        Pembahasan:<\/p>\n\n\n\n

        Dari persamaan pada soal, diketahui a<\/em> = -1, b<\/em> = -4, dan c<\/em> = c<\/em>. Untuk mencari nilai c<\/em>, gunakan persamaan nilai maksimum fungsi berikut.<\/p>\n\n\n\n

        \"\"<\/figure>\n\n\n\n

        Jadi, nilai konstanta c<\/em> adalah 12.<\/p>\n\n\n\n

        Jawaban: A<\/p>\n\n\n\n

        Contoh soal 4<\/strong><\/h3>\n\n\n\n

        Perhatikan persamaan berikut.<\/p>\n\n\n\n

        \"\"<\/figure>\n\n\n\n

        Koordinat titik potong terhadap sumbu-x adalah \u2026.<\/p>\n\n\n\n

          \n
        1. (-2, 0) dan (-1, 0)<\/li>\n\n\n\n
        2. (2, 0) dan (1, 0)<\/li>\n\n\n\n
        3. (-3, 0) dan (1, 0)<\/li>\n\n\n\n
        4. (4, 0) dan (2, 0)<\/li>\n<\/ol>\n\n\n\n

          Pembahasan:<\/p>\n\n\n\n

          Koordinat titik potong terhadap sumbu-x diperoleh jika y <\/em> = 0. Dengan demikian,<\/p>\n\n\n\n

          \"\"<\/figure>\n\n\n\n

          Jadi, koordinat titik potong terhadap sumbu-x adalah (2, 0) dan (1, 0).<\/p>\n\n\n\n

          Jawaban: B<\/p>\n\n\n\n

          Contoh soal 5<\/strong><\/h3>\n\n\n\n

          Pak Anton membeli sebidang tanah yang berbentuk persegipanjang. Panjang dan lebar tanah Pak Anton berturut-turut (2x<\/em> + 4) m dan (5 \u2013 x<\/em>) m. Luas maksimum tanah tersebut adalah \u2026.<\/p>\n\n\n\n

            \n
          1. 24,5 m2<\/sup><\/li>\n\n\n\n
          2. 12,4 m2<\/sup><\/li>\n\n\n\n
          3. 30,8 m2<\/sup><\/li>\n\n\n\n
          4. 42,5 m2<\/sup><\/li>\n<\/ol>\n\n\n\n

            Pembahasan:<\/p>\n\n\n\n

            Mula-mula, kamu harus mencari fungsi luas tanah yang dibeli Pak Anton. Gunakan persamaan luas persegipanjang, ya.<\/p>\n\n\n\n

            \"\"<\/figure>\n\n\n\n

            Dari fungsi di atas, diperoleh a<\/em> = -2, b<\/em> = 6, dan c<\/em> = 20.<\/p>\n\n\n\n

            Untuk mencari luas maksimum, gunakan persamaan berikut.<\/p>\n\n\n\n

            \"\"<\/figure>\n\n\n\n

            Jadi, luas maksimum tanah yang dibeli Pak Anton adalah 24,5 m2<\/sup>.<\/p>\n\n\n\n

            Contoh soal 6<\/strong><\/h3>\n\n\n\n

            Figo melemparkan bola secara vertikal ke atas. Lemparan bola itu membentuk persamaan <\/sub>. Dalam waktu 2 s, berapa ketinggian bolanya?<\/p>\n\n\n\n

            Pembahasan:<\/p>\n\n\n\n

            Untuk mencari ketinggian bola dalam waktu 2 s, kamu hanya perlu mensubstitusikan t<\/em> = 2 s ke persamaan ketinggian (h<\/em>(t<\/em>)).<\/p>\n\n\n\n

            \"\"<\/figure>\n\n\n\n

            Jadi, ketinggian bolanya dalam waktu 2 s adalah 5 m.<\/p>\n\n\n\n

            Contoh soal 7<\/strong><\/h3>\n\n\n\n

            Jumlah antara k<\/em> dan l<\/em> adalah 15. Tentukan fungsi kuadrat yang bisa dibentuk oleh hasil kali kedua bilangan tersebut!<\/p>\n\n\n\n

            Pembahasan:<\/p>\n\n\n\n

            Mula-mula, kamu harus menjabarkan maksud soal dalam bentuk persamaan.<\/p>\n\n\n\n

            Jumlah antara k<\/em> dan l<\/em> jika dinyatakan secara matematis menjadi seperti berikut.<\/p>\n\n\n\n

            \"\"<\/figure>\n\n\n\n

            Untuk mencari fungsi kuadrat dari kedua variabel tersebut, lakukan perkalian antarvariabelnya.<\/p>\n\n\n\n

            \"\"<\/figure>\n\n\n\n

            Jadi, fungsi yang bisa dibentuk adalah f<\/em>(l<\/em>) = 15l<\/em> \u2013 l<\/em>2<\/sup> atau f<\/em>(k<\/em>) = 15k<\/em> \u2013 k<\/em>2<\/sup>.<\/p>\n\n\n\n

            Contoh soal 8<\/strong><\/h3>\n\n\n\n

            Perhatikan persamaan berikut.<\/p>\n\n\n\n

            \"\"<\/figure>\n\n\n\n

            Tentukan sumbu simetri grafik fungsi tersebut!<\/p>\n\n\n\n

            Pembahasan:<\/p>\n\n\n\n

            Dari persamaan tersebut diketahui a<\/em> = 4, b<\/em> = -2, dan c<\/em> = 7.<\/p>\n\n\n\n

            Untuk sumbu simetri bisa kamu tentukan dengan persamaan berikut.<\/p>\n\n\n\n

            \"\"<\/figure>\n\n\n\n

            Jadi, sumbu simetri grafik fungsi tersebut adalah <\/sub>.<\/p>\n\n\n\n

            Contoh soal 9<\/strong><\/h3>\n\n\n\n

            Sebuah grafik fungsi <\/sub>memotong sumbu-x di (2, 0). Berapakah nilai k<\/em>?<\/p>\n\n\n\n

            Pembahasan:<\/p>\n\n\n\n

            Ingat, jika memotong sumbu-x maka nilai fungsinya harus nol (y<\/em> = 0). Dengan demikian:<\/p>\n\n\n\n

            \"\"<\/figure>\n\n\n\n

            Jadi, nilai k<\/em> = -4.<\/p>\n\n\n\n

            Contoh soal 10<\/strong><\/h3>\n\n\n\n

            Sebuah industri rumahan mampu memproduksi baju sebanyak <\/sub>potong baju selama sehari. Berapakah jumlah produksi baju minimum yang mampu dihasilkan dalam kurun waktu x<\/em> hari?<\/p>\n\n\n\n

            Pembahasan:<\/p>\n\n\n\n

            Mula-mula, kamu harus mencari fungsi banyaknya baju yang bisa diproduksi selama x<\/em> hari.<\/p>\n\n\n\n

            \"\"<\/figure>\n\n\n\n

            Oleh karena a<\/em> > 0, maka fungsi di atas memiliki nilai minimum dan diperoleh a<\/em> = 1, b<\/em> = -40, dan c<\/em> = 500.<\/p>\n\n\n\n

            Untuk mencari jumlah produksi baju minimum selama x<\/em> hari, gunakan persamaan berikut.<\/p>\n\n\n\n

            \"\"<\/figure>\n\n\n\n

            Jadi, selama x<\/em> hari industri rumahan itu mampu menghasilkan minimal 100 potong baju.<\/p>\n\n\n\n

            Itulah beberapa contoh soal terkait fungsi kuadrat yang bisa kamu jadikan referensi belajar. Semoga bermanfaat, ya. Jika ingin melihat contoh soal lainnya, yuk buruan gabung Quipper Video. Bersama Quipper Video, belajar jadi lebih mudah dan seru! Salam Quipper!<\/p>\n","protected":false},"excerpt":{"rendered":"

            Hai Quipperian, tahukah kamu kedudukan fungsi di dalam Matematika itu sama seperti kedudukan garam di dalam masakan. Hampir setiap permasalahan di dalam Matematika melibatkan…<\/p>\n","protected":false},"author":99400369,"featured_media":308284,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"_crdt_document":"","_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[679384888,679384865],"tags":[679385363],"ppma_author":[679386827,679386836],"class_list":["post-230091","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mapel","category-matematika","tag-matematika-kelas-9"],"acf":[],"yoast_head":"\nContoh Soal Fungsi Kuadrat Lengkap dengan Pembahasan - Quipper Blog<\/title>\n<meta name=\"description\" content=\"Kuasai materi fungsi kuadrat lebih cepat dengan mengerjakan soal latihan ini. 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