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[
{
"slide": 1,
"fragments": [
{
"fragment_index": -1,
"text_description": "What is a Quadratic Equation?",
"image_description": ""
},
{
"fragment_index": 1,
"text_description": "Quadratic Equation",
"image_description": ""
},
{
"fragment_index": 2,
"text_description": "A quadratic equation is any equation that can be written in the standard form \\(ax^2 + bx + c = 0\\) where \\(a \\neq 0\\).\nIt is called “quadratic” because the highest power of the variable is 2.",
"image_description": ""
}
]
},
{
"slide": 2,
"fragments": [
{
"fragment_index": -1,
"text_description": "Graph of a Quadratic Function\nWhat shape do we get?\nPlotting \\(y = x^{2}\\) joins the points into a smooth U-shape.\nThis U-shaped curve is called a\nparabola\n. Every quadratic graph \\(y = ax^{2}+bx+c\\) forms a parabola.",
"image_description": ""
},
{
"fragment_index": 1,
"text_description": "Parabola for y = x²\nA smooth curve opening upwards.\n.axis{stroke:#555;stroke-width:1}\n .curve{fill:none;stroke:#1d4ed8;stroke-width:2}\n .label{font-size:12px;fill:#555;font-family:Roboto, sans-serif}\nx\ny\nA smooth curve opening upwards.",
"image_description": "https://sparkl-vector-images.s3.ap-south-1.amazonaws.com/presentation_images/media.slid.es/uploads/2766130/images/11524831/Fig.1.png"
},
{
"fragment_index": 2,
"text_description": "Key Points:\nU-shaped curve is called a\nparabola\n.\nAll graphs of \\(y = ax^{2} + bx + c\\) are parabolas.",
"image_description": ""
}
]
},
{
"slide": 3,
"fragments": [
{
"fragment_index": -1,
"text_description": "Roots as X-Intercepts",
"image_description": ""
},
{
"fragment_index": 1,
"text_description": "y = x² − 6x + 8\nX-intercepts at x = 2 and x = 4 represent the roots.\n2\n4\ny\nx\nX-intercepts at x = 2 and x = 4 represent the roots.",
"image_description": "https://sparkl-vector-images.s3.ap-south-1.amazonaws.com/presentation_images/media.slid.es/uploads/2766130/images/11524831/Fig.1.png"
},
{
"fragment_index": 2,
"text_description": "Graphical Meaning of Roots\nA root is any x-value where the parabola meets the x-axis, so \\(y = 0\\).\nOn this graph, the quadratic \\(y = x^{2} - 6x + 8\\) touches the axis at \\(x = 2\\) and \\(x = 4\\).",
"image_description": ""
},
{
"fragment_index": 3,
"text_description": "Key Points:\nRoots are the solutions of the quadratic equation.\nThey appear graphically where the curve crosses the x-axis.",
"image_description": ""
}
]
},
{
"slide": 4,
"fragments": [
{
"fragment_index": -1,
"text_description": "Procedure to Solve by Graphing\nFollow these steps to obtain the roots of a quadratic equation from its graph.",
"image_description": ""
},
{
"fragment_index": 1,
"text_description": "1\nPrepare a value table\nSelect several x-values and calculate corresponding y = ax² + bx + c.",
"image_description": ""
},
{
"fragment_index": 2,
"text_description": "2\nPlot the computed points\nMark each (x, y) accurately on graph paper with equal units.",
"image_description": ""
},
{
"fragment_index": 3,
"text_description": "3\nDraw the parabola\nConnect the points smoothly to form the quadratic curve.",
"image_description": ""
},
{
"fragment_index": 4,
"text_description": "4\nLocate the x-intercepts\nIdentify where the curve intersects the x-axis.",
"image_description": ""
},
{
"fragment_index": 5,
"text_description": "5\nWrite the roots\nThe x-coordinates of the intercepts are the equation’s solutions.",
"image_description": ""
},
{
"fragment_index": 6,
"text_description": "Pro Tip:\nChoose x-values symmetrically around the vertex for a balanced, accurate graph.",
"image_description": ""
}
]
},
{
"slide": 5,
"fragments": [
{
"fragment_index": -1,
"text_description": "Worked Example: x² − 5x + 6 = 0\ny = x² − 5x + 6\nGraph of y = x² − 5x + 6\nRoots appear where the curve meets the x-axis at x = 2 and x = 3.\nx\ny\nRoots at x = 2 and x = 3.",
"image_description": ""
},
{
"fragment_index": 1,
"text_description": "Key Insights\n1. Plot ordered pairs for \\(x = 0\\) to \\(5\\).\n2. Join points smoothly to form the parabola.\n3. Curve intersects the x-axis at \\(x = 2\\) and \\(x = 3\\).\n4. Therefore, the roots of the quadratic are 2 and 3.",
"image_description": ""
},
{
"fragment_index": 2,
"text_description": "Legend\nParabola \\(y = x^{2}-5x+6\\)\nRoots",
"image_description": ""
}
]
},
{
"slide": 6,
"fragments": [
{
"fragment_index": -1,
"text_description": "Check Your Understanding\nQuestion\nFrom the graph shown, what are the roots of the quadratic equation? Identify the x-intercepts.\nHint:\nRoots are the x-coordinates where the curve meets the x-axis (y = 0).\nSubmit Answer\nCorrect!\nYes — the graph crosses the x-axis at x = 2 and x = 3.\nIncorrect\nRe-examine where the curve touches the x-axis; those points give the roots.\n// MCQ interaction logic\n const correctOption = 1; // 0-based index for option \"2 and 3\"\n const answerCards = document.querySelectorAll('.answer-card');\n const submitBtn = document.querySelector('#slide-07-h3f9bq-submit button');\n const feedbackCorrect = document.getElementById('feedbackCorrect');\n const feedbackIncorrect = document.getElementById('feedbackIncorrect');\n\n let selectedOption = null;\n\n answerCards.forEach((card, index) => {\n card.addEventListener('click', () => {\n answerCards.forEach(c => c.classList.remove('border-blue-500', 'bg-blue-50'));\n card.classList.add('border-blue-500', 'bg-blue-50');\n selectedOption = index;\n });\n });\n\n submitBtn.addEventListener('click', () => {\n if (selectedOption === null) return;\n\n if (selectedOption === correctOption) {\n feedbackCorrect.classList.remove('hidden');\n feedbackIncorrect.classList.add('hidden');\n } else {\n feedbackIncorrect.classList.remove('hidden');\n feedbackCorrect.classList.add('hidden');\n }\n });",
"image_description": ""
},
{
"fragment_index": 1,
"text_description": "1\n1 and 5",
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},
{
"fragment_index": 2,
"text_description": "2\n2 and 3",
"image_description": ""
},
{
"fragment_index": 3,
"text_description": "3\n3 and 4",
"image_description": ""
},
{
"fragment_index": 4,
"text_description": "4\n0 and 6",
"image_description": ""
}
]
},
{
"slide": 7,
"fragments": [
{
"fragment_index": -1,
"text_description": "Special Root Scenarios",
"image_description": ""
},
{
"fragment_index": 1,
"text_description": "Graphical view of root scenarios",
"image_description": "https://sparkl-vector-images.s3.ap-south-1.amazonaws.com/presentation_images/asset.sparkl.me/pb/presentation/495/images/31bc7c96de208de32a21c13f527b2b15.png"
},
{
"fragment_index": 2,
"text_description": "Reading the x-axis\nCount the parabola's hits on the x-axis to determine its real roots.\nThis visual cue separates two, one, and zero-root cases at a glance.",
"image_description": ""
},
{
"fragment_index": 3,
"text_description": "Key Points:\nTwo roots – curve crosses the x-axis twice.\nOne root – curve touches the x-axis only at its vertex.\nNo real roots – curve stays entirely above or below the x-axis.",
"image_description": ""
}
]
},
{
"slide": 8,
"fragments": [
{
"fragment_index": -1,
"text_description": "Key Takeaways",
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},
{
"fragment_index": 1,
"text_description": "Every quadratic equation plots as a U-shaped parabola.",
"image_description": ""
},
{
"fragment_index": 2,
"text_description": "Roots are the x-intercepts where \\(y = 0\\).",
"image_description": ""
},
{
"fragment_index": 3,
"text_description": "Plot a few precise points to reveal those intercepts.",
"image_description": ""
},
{
"fragment_index": 4,
"text_description": "The parabola’s position shows whether there are two, one, or no real solutions.",
"image_description": ""
},
{
"fragment_index": 5,
"text_description": "Thank You!\nThese points consolidate the graphical solution method.",
"image_description": ""
}
]
}
]