A stone is thrown from a cliff into the sea. Its height, \(y\) metres, above the sea level at time \(x\) seconds is given by \(y=-x^2+2x+9\).
Express \(y\) in the form of \(y=a(x-h)^2+k\). Hence state the maximum height of the stone above the sea level and the time taken to reach this height.[4]
Hence or otherwise, solve the equation \(-x^2+2x+9=0\). Explain the significance of the positive value of \(x\).[4]
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Answer:(a) \(y=-(x-1)^2+10\); 10 m at 1 s. (b) \(x=1\pm\sqrt{10}\); the stone reaches sea level after \(4.16\) s.