<ol class="abc-list"><li><div class="list-item-paragraph">Express $y = 5 - 12x - 3x^2$ in the form $y = a(x + b)^2 + c$ and hence show that $y$ can never be greater than $20$.<span class="inline-marks">[3]</span></div></li><li><div class="list-item-paragraph">Explain why there are no values of $k$ for which the curve $y = (k - 1)x^2 + 2(k + 2)x + k + 3$ is always positive.<span class="inline-marks">[4]</span></div></li></ol>

Express $y = 5 - 12x - 3x^2$ in the form $y = a(x + b)^2 + c$ and hence show that $y$ can never be greater than $20$.

Explain why there are no values of $k$ for which the curve $y = (k - 1)x^2 + 2(k + 2)x + k + 3$ is always positive.

Quadratic Expressions, Equations, and Functions - Solving Quadratic Equation by Completing the Square

Quadratic Expressions, Equations, and Functions - Solving Quadratic Equation by Completing the Square