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<p>The table below shows experimental values of two variables \(x\) and \(y\) which are connected by an equation of the form \(ax^2 + by = 1\), where&nbsp;\(a\) and \(b\) are constants.</p>
<div class="content-block content-block--table"><div class="table-container"><table style="table-layout: fixed; width: 490px;"><colgroup><col style="width: 70px;"><col style="width: 70px;"><col style="width: 70px;"><col style="width: 70px;"><col style="width: 70px;"><col style="width: 70px;"><col style="width: 70px;"></colgroup><thead><tr><th style="text-align: center; --cell-justify: center">\(x\)</th><th style="text-align: center; --cell-justify: center">\(1\)</th><th style="text-align: center; --cell-justify: center">\(2\)</th><th style="text-align: center; --cell-justify: center">\(3\)</th><th style="text-align: center; --cell-justify: center">\(4\)</th><th style="text-align: center; --cell-justify: center">\(5\)</th><th style="text-align: center; --cell-justify: center">\(6\)</th></tr></thead><tbody><tr><td style="text-align: center; --cell-justify: center">\(y\)</td><td style="text-align: center; --cell-justify: center">\(0.47\)</td><td style="text-align: center; --cell-justify: center">\(0.87\)</td><td style="text-align: center; --cell-justify: center">\(1.53\)</td><td style="text-align: center; --cell-justify: center">\(2.47\)</td><td style="text-align: center; --cell-justify: center">\(3.87\)</td><td style="text-align: center; --cell-justify: center">\(5.14\)</td></tr></tbody></table></div></div>
<p>Using a suitable scale, plot the graph of \(y\) against \(x^2\). Use your graph to</p>
<ol class="i-list"><li data-list-item-id="item-i" data-list-item-path="item-i"><div class="list-item-content"><span class="list-item-text">determine which value of \(y\) is inaccurate and estimate its correct value,</span></div></li><li data-list-item-id="item-ii" data-list-item-path="item-ii"><div class="list-item-content"><span class="list-item-text">estimate the value of \(a\) and of \(b\).</span></div></li><li data-list-item-id="item-iii" data-list-item-path="item-iii"><div class="list-item-paragraph">By drawing a suitable straight line, find the values of \(x\) and \(y\) which satisfy the following pair of simultaneous equations.</div><div class="list-item-paragraph" style="text-align: center">\(ax^2 + by = 1\)<br>\(2x^2 + y = 3\)</div></li></ol>
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The table below shows experimental values of two variables \(x\) and \(y\) which are connected by an equation of the form \(ax^2 + by = 1\), where \(a\) and \(b\) are constants.

Using a suitable scale, plot the graph of \(y\) against \(x^2\). Use your graph to

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