<p>The equation of a curve is ${y = -x^2 + 2kx - k}$, where ${k}$ is a constant.</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">In the case where ${k = 3}$, find the set of values of ${x}$ for which the curve lies completely below the line ${y = 2}$.</span></div><p style="text-align: right;">[3]</p></li><li><div class="list-item-content"><span class="list-item-text">In the case where ${k < 0}$, explain if the line ${y = 2x + 1}$ is a tangent to the curve.</span></div><p style="text-align: right;">[3]</p></li></ol>

The equation of a curve is ${y = -x^2 + 2kx - k}$, where ${k}$ is a constant.

In the case where ${k = 3}$, find the set of values of ${x}$ for which the curve lies completely below the line ${y = 2}$.

In the case where ${k < 0}$, explain if the line ${y = 2x + 1}$ is a tangent to the curve.

2023 BTYSS 3AM EOY Q3

2023 BTYSS 3AM EOY Q3