0606 P13 - Nov 2022 - Q2 - 8 marks
7873
(a) Show that \(2x^2+x-15\) can be written in the form \(2(x+a)^2+b\), where \(a\) and \(b\) are exact constants to be found.
(b) Hence write down the coordinates of the stationary point on the curve \(y=2x^2+x-15\).
(c) On the axes, sketch the graph of
\(y=\left|2x^2+x-15\right|,\)
stating the coordinates of the points where the graph meets the coordinate axes.
(d) Write down the value of the constant \(k\) for which the equation
\(\left|2x^2+x-15\right|=k\)
has \(3\) distinct solutions.
