Line meets curve

Quadratic graph explorer

<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">Explain why the graph of ${y = -4x^2 + 4kx - (k^2 + 1)}$ lies entirely below the ${x}$-axis.</span></div><p style="text-align: right;">[3]</p></li><li><div class="list-item-content"><span class="list-item-text">Find the range of values of ${k}$ for which the line ${y = kx + 2}$ meets the curve ${x^2 + y^2 = 2}$.</span></div><p style="text-align: right;">[4]</p></li></ol>

Explain why the graph of ${y = -4x^2 + 4kx - (k^2 + 1)}$ lies entirely below the ${x}$-axis.

Find the range of values of ${k}$ for which the line ${y = kx + 2}$ meets the curve ${x^2 + y^2 = 2}$.

2023 ACS (BR) 3AM EOY Q7

2023 ACS (BR) 3AM EOY Q7