Quadratic Functions, Equations and Inequalities - Maximum and Minimum Values of General Quadratic Functions
Quadratic Functions, Equations and Inequalities - Maximum and Minimum Values of General Quadratic Functions
IP 3
Express \(y=-3{{x}^{2}}+6x-11\) in the form \(y=a{{(x+h)}^{2}}+k\) where \(a\), \(h\) and \(k\) are constants. State the maximum value of \(y\) and the corresponding value of \(x\). Hence sketch the graph of \(y=-3{{x}^{2}}+6x-11\) and state the coordinates of the maximum point of the curve.
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Answer:\(y=-3(x-1)^2-8\), so \(a=-3\), \(h=-1\), \(k=-8\); maximum \(-8\) at \(x=1\); maximum point \((1,-8)\); \(y\)-intercept \((0,-11)\); no real \(x\)-intercepts
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