Mathology
보통이차함수

이차함수 그래프의 꼭짓점 찾기

이차함수의 그래프의 꼭짓점 좌표를 구하고, 좌표의 합을 계산하는 문제입니다.

2026학년도 수능중학교 3학년

문제

이차함수 y=x2+4x1y = -x^2 + 4x - 1의 그래프의 꼭짓점의 좌표가 (p,q)(p, q)일 때, p+qp+q의 값은?

<!-- Background -->
<rect x="0" y="0" width="400" height="300" fill="#F8F7FF" />

<!-- Coordinate Axes -->
<line x1="10" y1="220" x2="380" y2="220" stroke="#1F2937" stroke-width="2" marker-end="url(#arrowhead)" />
<line x1="70" y1="20" x2="70" y2="290" stroke="#1F2937" stroke-width="2" marker-end="url(#arrowhead)" />

<!-- Axis Labels -->
<text x="375" y="215" font-family="'Noto Sans KR', sans-serif" font-size="14" fill="#1F2937" text-anchor="end">x</text>
<text x="75" y="25" font-family="'Noto Sans KR', sans-serif" font-size="14" fill="#1F2937" text-anchor="start">y</text>
<text x="55" y="235" font-family="'Noto Sans KR', sans-serif" font-size="14" fill="#1F2937" text-anchor="middle">O</text>

<!-- X-axis ticks and labels -->
<!-- x=1 -->
<line x1="105" y1="215" x2="105" y2="225" stroke="#1F2937" stroke-width="1" />
<text x="105" y="240" font-family="'Noto Sans KR', sans-serif" font-size="12" fill="#1F2937" text-anchor="middle">1</text>
<!-- x=2 -->
<line x1="140" y1="215" x2="140" y2="225" stroke="#1F2937" stroke-width="1" />
<text x="140" y="240" font-family="'Noto Sans KR', sans-serif" font-size="12" fill="#1F2937" text-anchor="middle">2</text>
<!-- x=3 -->
<line x1="175" y1="215" x2="175" y2="225" stroke="#1F2937" stroke-width="1" />
<text x="175" y="240" font-family="'Noto Sans KR', sans-serif" font-size="12" fill="#1F2937" text-anchor="middle">3</text>
<!-- x=4 -->
<line x1="210" y1="215" x2="210" y2="225" stroke="#1F2937" stroke-width="1" />
<text x="210" y="240" font-family="'Noto Sans KR', sans-serif" font-size="12" fill="#1F2937" text-anchor="middle">4</text>

<!-- Y-axis ticks and labels -->
<!-- y=1 -->
<line x1="65" y1="185" x2="75" y2="185" stroke="#1F2937" stroke-width="1" />
<text x="55" y="190" font-family="'Noto Sans KR', sans-serif" font-size="12" fill="#1F2937" text-anchor="end">1</text>
<!-- y=2 -->
<line x1="65" y1="150" x2="75" y2="150" stroke="#1F2937" stroke-width="1" />
<text x="55" y="155" font-family="'Noto Sans KR', sans-serif" font-size="12" fill="#1F2937" text-anchor="end">2</text>
<!-- y=3 -->
<line x1="65" y1="115" x2="75" y2="115" stroke="#1F2937" stroke-width="1" />
<text x="55" y="120" font-family="'Noto Sans KR', sans-serif" font-size="12" fill="#1F2937" text-anchor="end">3</text>

<!-- Parabola Curve -->
<!-- Math points: (0,-1), (2,3) vertex, (4,-1) -->
<!-- Control points for Q: (1,3), (3,3) -->
<path d="M 70 255 Q 105 115 140 115 Q 175 115 210 255" fill="none" stroke="#1F2937" stroke-width="2" />

<!-- Vertex Point -->
<circle cx="140" cy="115" r="4" fill="#1F2937" />
<text x="145" y="105" font-family="'Noto Sans KR', sans-serif" font-size="14" fill="#1F2937" text-anchor="start">(p, q)</text>
<!-- Coordinates for the vertex -->
<text x="145" y="125" font-family="'Noto Sans KR', sans-serif" font-size="12" fill="#1F2937" text-anchor="start">(2, 3)</text>

<!-- Equation Label -->
<text x="250" y="180" font-family="'Noto Sans KR', sans-serif" font-size="14" fill="#1F2937" text-anchor="start">y = -x² + 4x - 1</text>
🔐

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#이차함수#꼭짓점#그래프의 평행이동#완전제곱식#수학#이차함수
이차함수 그래프의 꼭짓점 찾기 - 이차함수 풀이 | Mathology