Further Pure Math 9-1 4PM1: The quadratic function Topical Past Paper Questions

(a) Use algebra to find the x coordinates of the points where the curve with equation $ y=3x^{2}+9x-17 $ intersects the line with equation y=3-2x (3) (b) Hence, or otherwise, find the set of values of x for which $3-2x \leqslant 3x^{2}+9x-17$ (2)

$$ \mathrm{f}(x)=3-4x-9x^{2} $$ Given that $f(x)$ can be expressed in the form $A-B(x+C)^{2}$ where $A, B$ and $C$ are positive constants (a) find the value of $A$, the value of $B$ and the value of $C$ (4) (b) Hence write down the maximum value of $f(x)$ (1) The equation $ f(x)=…

$$ \mathrm{f}(x)=2x^{2}+5x-p $$ The equation $ f(x) = 0 $ has roots $ \alpha $ and $ \beta $. Given that $ \alpha^{3} + \beta^{3} = -\frac{215}{8} $ (a) find the value of $p$ (5) Without solving the equation $ f(x) = 0 $ (b) form a quadratic equation, with integer coefficients, t…