The equation of a curve is \(y=2x^2-8x+11\). By expressing the curve in the form of \(y=a(x+b)^2+c\), where \(a\), \(b\) and \(c\) are constants, find the coordinates of the stationary point on the curve.[2]
Hence or otherwise, find the range of values of the constant \(k\) such that the equation \(2x^2-8x+11=k\) does not have 2 distinct roots.[2]
The equation of a curve is \(y=p(x-q)^2+r\), where \(p\), \(q\) and \(r\) are constants. The curve intersects with the \(x\)-axis at \((2,0)\) and \((4,0)\) and the maximum value of \(y\) is 2. Find the values of \(p\), \(q\) and \(r\).[4]
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Answer:(a)(i) \(y=2(x-2)^2+3\), stationary point \((2,3)\). (ii) \(k\le3\). (b) \(p=-2,q=3,r=2\).