<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">The curve with equation \(y = ax^2 + bx + a\), where \(a\) and \(b\) are constants, lies completely above the \(x\)-axis.</span></div><ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Write down the conditions which must apply to \(a\) and \(b\).</span><span class="inline-marks">[2]</span></div></li><li><div class="list-item-paragraph">Give an example of possible values for \(a\) and \(b\) which satisfy the conditions in part <strong>(i)</strong>.<span class="inline-marks">[2]</span></div></li></ol></li><li><div class="list-item-content"><span class="list-item-text">Using a suitable substitution, explain why the equation \(3^{2x-1} = 3^{x+2} - k\) has no solution if \(k &gt; 60.75\).</span><span class="inline-marks">[3]</span></div></li></ol>

The curve with equation \(y = ax^2 + bx + a\), where \(a\) and \(b\) are constants, lies completely above the \(x\)-axis.

Write down the conditions which must apply to \(a\) and \(b\).

Give an example of possible values for \(a\) and \(b\) which satisfy the conditions in part (i).

Using a suitable substitution, explain why the equation \(3^{2x-1} = 3^{x+2} - k\) has no solution if \(k > 60.75\).

2023 Ahmad Ibrahim Sec 3 AM EOY Q6

2023 Ahmad Ibrahim Sec 3 AM EOY Q6

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