{"id":848,"date":"2026-04-25T21:38:34","date_gmt":"2026-04-25T18:38:34","guid":{"rendered":"https:\/\/www.riyaziyeci.com\/?page_id=848"},"modified":"2026-04-26T00:06:20","modified_gmt":"2026-04-25T21:06:20","slug":"parabol-genel-degerlendirme","status":"publish","type":"page","link":"https:\/\/www.riyaziyeci.com\/?page_id=848","title":{"rendered":"Parabol Genel De\u011ferlendirme"},"content":{"rendered":"    <style>\n        .osym-container { width: 100%; max-width: 900px; margin: 0 auto; padding: 15px; font-family: 'Times New Roman', Times, serif; background: #fff; box-sizing: border-box; }\n        .osym-header { border-bottom: 4px solid #16a085; padding-bottom: 15px; margin-bottom: 25px; text-align: center; }\n        .osym-header h2 { font-size: 24px; color: #1a1a1a; font-weight: bold; margin: 0 0 10px 0; letter-spacing: 1px; text-transform: uppercase; }\n        .osym-subtitle { font-size: 14px; color: #7f8c8d; font-family: Arial, sans-serif; font-weight: bold; margin-bottom: 15px; }\n        \n        .top-actions { display: flex; justify-content: center; gap: 15px; flex-wrap: wrap; margin-bottom: 20px; }\n        .btn-action { background: #16a085; color: #fff; border: none; padding: 10px 20px; font-size: 15px; font-weight: bold; border-radius: 5px; cursor: pointer; transition: 0.3s; font-family: Arial, sans-serif; }\n        .btn-action:hover { background: #117a65; }\n        .btn-pdf { background: #c0392b; } .btn-pdf:hover { background: #902b20; }\n        .btn-panel { background: #2c3e50; } .btn-panel:hover { background: #1a252f; }\n        \n        #osym-questions-area { display: block; width: 100%; clear: both; }\n        \n        .osym-card { border: 1px solid #dcdcdc; padding: 35px 20px 20px 20px; margin-bottom: 40px; position: relative; width: 100%; box-sizing: border-box; box-shadow: 0 5px 15px rgba(0,0,0,0.05); background: #fff; }\n        .osym-q-no { position: absolute; top: -15px; left: 15px; background: #1a1a1a; color: #fff; padding: 6px 16px; font-size: 14px; 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font-size: 13px; }\n        .btn-kolay { background: #e8f8f5; color: #1abc9c; border-color: #1abc9c; }\n        .btn-kolay:hover, .btn-kolay.active { background: #1abc9c; color: #fff; }\n        .btn-zor { background: #fdedec; color: #e74c3c; border-color: #e74c3c; }\n        .btn-zor:hover, .btn-zor.active { background: #e74c3c; color: #fff; }\n        \n        .osym-btn-sol { background: #fff; color: #1a1a1a; border: 2px solid #1a1a1a; padding: 10px 20px; font-weight: bold; font-family: Arial, sans-serif; cursor: pointer; transition: 0.3s; width: 100%; font-size: 14px; margin-top: 15px; }\n        .osym-btn-sol:hover { background: #1a1a1a; color: #fff; }\n        .osym-sol-box { display: none; margin-top: 20px; padding: 15px; background: #fdfbfb; border-left: 5px solid #16a085; font-size: 15px; line-height: 1.6; color: #1a1a1a; overflow-x: auto; }\n\n        \/* \u00d6\u011frenci Paneli Modal (Popup) *\/\n        #student-dashboard { display: none; position: fixed; top: 0; left: 0; width: 100%; height: 100%; background: rgba(0,0,0,0.8); z-index: 9999; justify-content: center; align-items: center; padding: 20px; box-sizing: border-box; font-family: Arial, sans-serif; }\n        .dashboard-content { background: #fff; width: 100%; max-width: 600px; padding: 30px; border-radius: 10px; position: relative; text-align: center; }\n        .close-dash { position: absolute; top: 15px; right: 20px; font-size: 24px; cursor: pointer; font-weight: bold; color: #333; }\n        .dash-stats { display: flex; justify-content: space-around; margin: 20px 0; }\n        .stat-box { padding: 15px; border-radius: 8px; width: 45%; }\n        .stat-box.success { background: #e8f8f5; color: #27ae60; border: 1px solid #27ae60; }\n        .stat-box.danger { background: #fdedec; color: #c0392b; border: 1px solid #c0392b; }\n        .stat-box h3 { margin: 0 0 5px 0; font-size: 28px; }\n        .stat-box p { margin: 0; font-size: 13px; font-weight: bold; }\n\n        \/* A4 KA\u011eIDINA 4 SORU SI\u011eDIRAN KUSURSUZ MATBAA D\u0130ZG\u0130S\u0130 *\/\n        @media print {\n            @page { size: A4 portrait; margin: 10mm; }\n            body { background: #fff; }\n            body * { visibility: hidden; }\n            #osym-app, #osym-app * { visibility: visible; }\n            #osym-app { position: absolute; left: 0; top: 0; width: 100%; padding: 0; margin: 0; }\n            \n            .osym-header, .top-actions, .osym-btn-sol, .osym-sol-box, .student-actions, #student-dashboard { display: none !important; }\n            \n            #osym-questions-area { display: block; width: 100%; }\n            \n            .osym-card { \n                visibility: visible;\n                float: left;\n                width: 48%; \/* 2 S\u00fctun *\/\n                height: 13.5cm; \/* A4 boyunun yar\u0131s\u0131 *\/\n                margin: 0 4% 1cm 0; \n                padding: 25px 15px 10px 15px;\n                border: 1px solid #999;\n                box-shadow: none;\n                page-break-inside: avoid;\n                overflow: hidden;\n            }\n            .osym-card:nth-child(2n) { margin-right: 0; }\n            .osym-card:nth-child(2n+1) { clear: left; }\n            .osym-card:nth-child(4n) { page-break-after: always; margin-bottom: 0; } \/* Her 4 soruda bir yeni sayfa *\/\n            \n            .osym-canvas-wrap { height: 160px !important; margin-bottom: 10px; }\n            .osym-text { font-size: 14px; }\n            .osym-tag { font-size: 10px; padding: 4px 8px; }\n        }\n    <\/style>\n\n    <div id=\"student-dashboard\">\n        <div class=\"dashboard-content\">\n            <span class=\"close-dash\" onclick=\"document.getElementById('student-dashboard').style.display='none'\">&times;<\/span>\n            <h2 style=\"color: #2c3e50; margin-top:0;\">\u00d6\u011frenci Geli\u015fim Analizi<\/h2>\n            <p style=\"color: #7f8c8d; font-size:14px;\">G\u00fcrkan Teacher AYT Sistemindeki Genel Performans\u0131n<\/p>\n            \n            <div class=\"dash-stats\">\n                <div class=\"stat-box success\">\n                    <h3 id=\"stat-kolay\">0<\/h3>\n                    <p>\u00c7\u00d6Z\u00dcLEB\u0130LEN SORU<\/p>\n                <\/div>\n                <div class=\"stat-box danger\">\n                    <h3 id=\"stat-zor\">0<\/h3>\n                    <p>ZORLANILAN SORU<\/p>\n                <\/div>\n            <\/div>\n            <button class=\"btn-action\" style=\"margin-top:20px; width:100%; background:#e74c3c;\" onclick=\"sifirlaVerileri()\">\ud83d\uddd1\ufe0f Analiz Verilerimi S\u0131f\u0131rla<\/button>\n        <\/div>\n    <\/div>\n\n    <div class=\"osym-container\" id=\"osym-app\">\n        <div class=\"osym-header\">\n            <h2>2018-2025 AYT \u00c7IKMI\u015e SORU \u0130K\u0130ZLER\u0130 DENEMES\u0130<\/h2>\n            <div class=\"osym-subtitle\">G\u00fcrkan I\u015eIK Matematik \u00d6\u011fretmeni | Her yenilemede kurgular de\u011fi\u015fir.<\/div>\n            <div class=\"top-actions\">\n                <button class=\"btn-action btn-panel\" onclick=\"paneliAc()\">\ud83d\udcca \u00d6\u011frenci Panelimi A\u00e7<\/button>\n                <button class=\"btn-action btn-pdf\" onclick=\"window.print()\">\ud83d\udda8\ufe0f A4 Test F\u00f6y\u00fc Olarak \u0130ndir (4 Soru\/Sayfa)<\/button>\n            <\/div>\n        <\/div>\n        <div id=\"osym-questions-area\"><\/div>\n    <\/div>\n\n    <script>\n    \/\/ --- \u00d6\u011eRENC\u0130 VER\u0130 Y\u00d6NET\u0130M\u0130 ---\n    let ogrenciVerisi = JSON.parse(localStorage.getItem('riyaziyeci_ayt_data')) || { toplamKolay: 0, toplamZor: 0 };\n\n    function tepkiKaydet(btn, durum) {\n        let parent = btn.parentElement;\n        parent.querySelectorAll('.action-btn').forEach(b => b.classList.remove('active'));\n        btn.classList.add('active');\n\n        if(durum === 'kolay') ogrenciVerisi.toplamKolay++;\n        else ogrenciVerisi.toplamZor++;\n        \n        localStorage.setItem('riyaziyeci_ayt_data', JSON.stringify(ogrenciVerisi));\n    }\n\n    function sifirlaVerileri() {\n        if(confirm(\"T\u00fcm analiz verilerin silinecek. Emin misin?\")) {\n            ogrenciVerisi = { toplamKolay: 0, toplamZor: 0 };\n            localStorage.setItem('riyaziyeci_ayt_data', JSON.stringify(ogrenciVerisi));\n            paneliAc(); \n        }\n    }\n\n    function paneliAc() {\n        document.getElementById('student-dashboard').style.display = 'flex';\n        document.getElementById('stat-kolay').innerText = ogrenciVerisi.toplamKolay;\n        document.getElementById('stat-zor').innerText = ogrenciVerisi.toplamZor;\n    }\n\n    document.addEventListener('DOMContentLoaded', function() {\n        \n        function rasyonel(val) {\n            if (val === 1) return \"\"; if (val === -1) return \"-\";\n            if (val === 0.5) return \"\\\\frac{1}{2}\"; if (val === -0.5) return \"-\\\\frac{1}{2}\";\n            if (val === 0.25) return \"\\\\frac{1}{4}\"; if (val === -0.25) return \"-\\\\frac{1}{4}\";\n            return val;\n        }\n\n        function formul(a, b, c) {\n            let str = \"\";\n            if (a !== 0) str += rasyonel(a) + \"x^2\";\n            if (b > 0) str += \" + \" + (b === 1 ? \"x\" : rasyonel(b) + \"x\");\n            else if (b < 0) str += \" - \" + (b === -1 ? \"x\" : Math.abs(b) + \"x\");\n            if (c > 0) str += \" + \" + c; else if (c < 0) str += \" - \" + Math.abs(c);\n            return str;\n        }\n\n        function rastgele(min, max) { \n            return Math.floor(Math.random() * (max - min + 1)) + min;\n        }\n\n        \/\/ --- SONSUZ MOTOR: 2018-2025 \u00d6SYM TARZI \u0130K\u0130Z SORU FABR\u0130KALARI (TAMAMEN T\u00dcREVS\u0130Z) ---\n        const osymFabrika = [\n            function() { \/\/ AYT \u00d6TELEME TARZI\n                let a = [1, -1][rastgele(0,1)];\n                let r1 = rastgele(-3, 3); let k1 = rastgele(-4, 4);\n                let x_shift = rastgele(1, 4); let y_shift = rastgele(1, 4);\n                let yeni_r = r1 + x_shift; let yeni_k = k1 - y_shift;\n                let c_yeni = a * yeni_r * yeni_r + yeni_k;\n                return {\n                    tag: \"AYT \u00d6TELEME MANTI\u011eI\",\n                    q: `Dik koordinat d\u00fczleminde tepe noktas\u0131 $T_1(${r1}, ${k1})$ olan $f(x)$ parabol\u00fc veriliyor. Bu parabol $x$ ekseni boyunca pozitif y\u00f6nde $${x_shift}$ birim, $y$ ekseni boyunca negatif y\u00f6nde $${y_shift}$ birim \u00f6telenerek $g(x)$ parabol\u00fc elde ediliyor. $g(x)$ parabol\u00fcn\u00fcn ba\u015fkatsay\u0131s\u0131 $${a}$ oldu\u011funa g\u00f6re, $g(0)$ ka\u00e7t\u0131r?`,\n                    f: (x) => a * Math.pow(x - yeni_r, 2) + yeni_k,\n                    sol: `\u00d6teleme sonucu yeni tepe noktas\u0131 $T_2(${r1} + ${x_shift}, ${k1} - ${y_shift}) = T_2(${yeni_r}, ${yeni_k})$ olur.<br>Ba\u015fkatsay\u0131s\u0131 $${a}$ olan parabol denklemi: $g(x) = ${a === 1 ? \"\" : \"-\"}(x - (${yeni_r}))^2 + (${yeni_k})$<br>$x=0$ yazarsak $g(0) = ${a}(-${yeni_r})^2 + (${yeni_k}) = ${a * yeni_r * yeni_r} + (${yeni_k}) = ${c_yeni}$ bulunur.`\n                };\n            },\n            function() { \/\/ AYT K\u00d6K \u0130L\u0130\u015eK\u0130S\u0130\n                let r = rastgele(2, 5);\n                let a = [1, -1][rastgele(0,1)];\n                let b = -2 * a * r;\n                return {\n                    tag: \"AYT K\u00d6K \u0130L\u0130\u015eK\u0130S\u0130\",\n                    q: `$m$ bir ger\u00e7el say\u0131 olmak \u00fczere, $y = ${a===1?\"\":\"-\"}x^2 + ${b}x + m$ parabol\u00fcn\u00fcn $x$ eksenini kesti\u011fi noktalar $x_1$ ve $x_2$'dir. Bu parabol\u00fcn tepe noktas\u0131n\u0131n apsisi ka\u00e7t\u0131r?`,\n                    f: (x) => a * x * x + b * x - (a*r*r) + 2,\n                    sol: `Tepe noktas\u0131n\u0131n apsisi $r$, k\u00f6kler toplam\u0131n\u0131n yar\u0131s\u0131d\u0131r veya $r = \\\\frac{-b}{2a}$ form\u00fcl\u00fcyle do\u011frudan katsay\u0131lardan bulunur.<br>$r = \\\\frac{-(${b})}{2(${a})} = ${r}$ olarak bulunur.`\n                };\n            },\n            function() { \/\/ AYT KES\u0130\u015e\u0130M MANTI\u011eI\n                let a = [1, -1][rastgele(0,1)];\n                let k = rastgele(1, 4); \n                let dogru_y = rastgele(-2, 2);\n                let r = rastgele(-2, 3);\n                let m = dogru_y - a * k * k;\n                let b = -2 * a * r; let c = a * r * r + m;\n                return {\n                    tag: \"AYT KES\u0130\u015e\u0130M MANTI\u011eI\",\n                    q: `$f(x) = ${formul(a, b, c)}$ parabol\u00fc ile $y = ${dogru_y}$ do\u011frusu $A$ ve $B$ noktalar\u0131nda kesi\u015fmektedir. Buna g\u00f6re $|AB|$ uzunlu\u011fu ka\u00e7 birimdir?`,\n                    f: (x) => a*x*x + b*x + c,\n                    sol: `Kesi\u015fim noktalar\u0131 i\u00e7in denklemler e\u015fitlenir:<br>$${formul(a,b,c)} = ${dogru_y} \\\\Rightarrow ${formul(a,b,c - dogru_y)} = 0$<br>Bu denklem $${a === 1 ? \"\" : \"-\"}(x-(${r}))^2 - ${a*k*k} = 0$ \u015feklindedir.<br>$(x-(${r}))^2 = ${k*k} \\\\Rightarrow x-(${r}) = \\\\pm ${k} \\\\Rightarrow x_1 = ${r-k}, x_2 = ${r+k}$.<br>Uzakl\u0131k $|${r+k} - (${r-k})| = ${2*k}$ birimdir.`\n                };\n            },\n            function() { \/\/ AYT \u00c7\u0130FT PARABOL\n                let r1 = rastgele(-3, 2); let k1 = rastgele(1, 4);\n                let dx = 3; let dy = 4; \/\/ Pisagor \u00fc\u00e7l\u00fcs\u00fc ile tam say\u0131 mesafe garantisi\n                let r2 = r1 + dx; let k2 = k1 + dy;\n                return {\n                    tag: \"AYT \u00c7\u0130FT PARABOL\",\n                    q: `$y = (x-(${r1}))^2 + (${k1})$ ve $y = -(x-(${r2}))^2 + (${k2})$ parabolleri veriliyor. Bu iki parabol\u00fcn tepe noktalar\u0131 aras\u0131ndaki uzakl\u0131k ka\u00e7 birimdir?`,\n                    f: (x) => Math.pow(x-r1, 2) + k1,\n                    sol: `Birinci parabol\u00fcn tepe noktas\u0131 $T_1(${r1}, ${k1})$.<br>\u0130kinci parabol\u00fcn tepe noktas\u0131 $T_2(${r2}, ${k2})$.<br>\u0130ki nokta aras\u0131 uzakl\u0131k: $\\\\sqrt{(${r2} - (${r1}))^2 + (${k2} - (${k1}))^2}$<br>$= \\\\sqrt{(${dx})^2 + (${dy})^2} = \\\\sqrt{25} = 5$ birimdir.`\n                };\n            },\n            function() { \/\/ AYT YEN\u0130 NES\u0130L MODEL\n                let w = rastgele(3, 5); let taban = 2 * w;\n                let h = rastgele(4, 9);\n                let v = rastgele(1, w-1); \n                let a_str = `-\\\\frac{${h}}{${w*w}}`;\n                let arac_h_pay = h * (w*w - v*v); let arac_h_payda = w*w;\n                return {\n                    tag: \"YEN\u0130 NES\u0130L MODEL\",\n                    q: `Taban geni\u015fli\u011fi $${taban}$ metre ve en y\u00fcksek noktas\u0131 $${h}$ metre olan parabolik bir t\u00fcnelden, geni\u015fli\u011fi $${2*v}$ metre olan dikd\u00f6rtgen prizmas\u0131 \u015feklindeki bir kamyon ge\u00e7ecektir. Kamyonun y\u00fcksekli\u011fi en fazla ka\u00e7 metre olabilir?`,\n                    f: (x) => (-h\/(w*w)) * x * x + h,\n                    sol: `T\u00fcnelin tepe noktas\u0131n\u0131 $y$ ekseni \u00fczerinde al\u0131rsak $T(0, ${h})$ olur. Parabol $y = ax^2 + ${h}$ formundad\u0131r.<br>Taban $x$ ekseninde $[-${w}, ${w}]$ aral\u0131\u011f\u0131ndad\u0131r.<br>$0 = a(${w})^2 + ${h} \\\\Rightarrow a = ${a_str}$. Denklem: $y = ${a_str}x^2 + ${h}$.<br>Kamyonun sa\u011f k\u00f6\u015fesi $x = ${v}$ hizas\u0131ndan ge\u00e7er.<br>Maksimum y\u00fckseklik $y = ${a_str}(${v})^2 + ${h} = \\\\frac{${arac_h_pay}}{${arac_h_payda}}$ metre olur.`\n                };\n            },\n            function() { \/\/ AYT ALAN \u0130L\u0130\u015eK\u0130S\u0130\n                let k = rastgele(2, 5); let k_kare = k * k; let alan = k * k_kare;\n                return {\n                    tag: \"AYT ALAN \u0130L\u0130\u015eK\u0130S\u0130\",\n                    q: `$y = ${k_kare} - x^2$ parabol\u00fcn\u00fcn $x$ eksenini kesti\u011fi noktalar $A$ ve $B$, tepe noktas\u0131 $T$'dir. Buna g\u00f6re $ATB$ \u00fc\u00e7geninin alan\u0131 ka\u00e7 birimkaredir?`,\n                    f: (x) => k_kare - x*x,\n                    sol: `Parabol\u00fcn tepe noktas\u0131 $T(0, ${k_kare})$ oldu\u011fundan \u00fc\u00e7genin y\u00fcksekli\u011fi $${k_kare}$ birimdir.<br>$x$ eksenini kesti\u011fi noktalar: $${k_kare} - x^2 = 0 \\\\Rightarrow x = \\\\pm ${k}$.<br>\u00dc\u00e7genin taban\u0131 $|AB| = ${k} - (-${k}) = ${2*k}$ birimdir.<br>Alan $= \\\\frac{${2*k} \\\\times ${k_kare}}{2} = ${alan}$ birimkaredir.`\n                };\n            },\n            function() { \/\/ AYT TE\u011eETL\u0130K MANTI\u011eI\n                let a = [1, -1][rastgele(0,1)]; let m = rastgele(2, 6);\n                let b = -2 * a * m; let c = a * m * m;\n                return {\n                    tag: \"AYT TE\u011eETL\u0130K\",\n                    q: `$y = ${formul(a, b, c)}$ parabol\u00fcn\u00fcn grafi\u011fi $x$ eksenine te\u011fettir. Buna g\u00f6re parabol\u00fcn tepe noktas\u0131n\u0131n orijine olan uzakl\u0131\u011f\u0131 ka\u00e7 birimdir?`,\n                    f: (x) => a * Math.pow(x-m, 2),\n                    sol: `Parabol $x$ eksenine te\u011fet ise $\\\\Delta = 0$'d\u0131r ve tepe noktas\u0131 do\u011frudan $x$ ekseni \u00fczerindedir.<br>Tepe noktas\u0131n\u0131n apsisi $r = \\\\frac{-(${b})}{2(${a})} = ${m}$.<br>Ordinat $0$ oldu\u011fundan tepe noktas\u0131 $T(${m}, 0)$ olur. Orijine uzakl\u0131\u011f\u0131 $${m}$ birimdir.`\n                };\n            }\n        ];\n\n        let testSorulari = [];\n        for (let i = 0; i < 50; i++) {\n            testSorulari.push(osymFabrika[Math.floor(Math.random() * osymFabrika.length)]());\n        }\n\n        const container = document.getElementById('osym-questions-area');\n        testSorulari.forEach((item, index) => {\n            const card = document.createElement('div');\n            card.className = 'osym-card';\n            card.innerHTML = `\n                <div class=\"osym-q-no\">SORU ${index + 1}<\/div>\n                <div class=\"osym-tag\">${item.tag}<\/div>\n                <div class=\"osym-text\">${item.q}<\/div>\n                <div class=\"osym-canvas-wrap\"><canvas id=\"osym-c-${index}\"><\/canvas><\/div>\n                \n                <div class=\"student-actions\">\n                    <button class=\"action-btn btn-kolay\" onclick=\"tepkiKaydet(this, 'kolay')\">\ud83d\udc4d \u00c7\u00f6zd\u00fcm<\/button>\n                    <button class=\"action-btn btn-zor\" onclick=\"tepkiKaydet(this, 'zor')\">\ud83e\udd14 Zorland\u0131m<\/button>\n                <\/div>\n                \n                <button class=\"osym-btn-sol\" onclick=\"const s=this.nextElementSibling; s.style.display=s.style.display==='block'?'none':'block'\">G\u00fcrkan Teacher'\u0131n \u00c7\u00f6z\u00fcm\u00fc<\/button>\n                <div class=\"osym-sol-box\"><strong>Analitik \u00c7\u00f6z\u00fcm (T\u00fcrevsiz):<\/strong><br>${item.sol}<\/div>\n            `;\n            container.appendChild(card);\n\n            const ctx = document.getElementById(`osym-c-${index}`).getContext('2d');\n            new Chart(ctx, {\n                type: 'line',\n                data: {\n                    datasets: [{\n                        data: Array.from({length: 161}, (_, j) => {\n                            let x = -8 + (j * 0.1); \n                            return {x: x, y: item.f(x)};\n                        }),\n                        borderColor: '#1a1a1a', \n                        borderWidth: 2.5, pointRadius: 0, tension: 0, fill: false\n                    }]\n                },\n                options: {\n                    responsive: true, maintainAspectRatio: false, events: [],\n                    layout: { padding: 5 },\n                    scales: {\n                        x: { type: 'linear', position: 'center', min: -8, max: 8, ticks: { stepSize: 1, color: '#000', font: { size: 9 }, callback: function(v) { return v === 0 ? 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