Sketch the graph of \(y=4{{x}^{2}}+13x+3\), indicate clearly the turning point and cutting point(s) on the axes. Hence, find the maximum or minimum point of the function and the value of \(x\) where it occurs, the equation of the line of symmetry of the graph.

Quadratic Functions, Equations and Inequalities - Maximum and Minimum Values of General Quadratic Functions

Secondary 3

Sketch the graph of \(y=4{{x}^{2}}+13x+3\), indicate clearly the turning point and cutting point(s) on the axes.

Hence, find

the maximum or minimum point of the function and the value of \(x\) where it occurs,
the equation of the line of symmetry of the graph.

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Answer:(i) Minimum point \(\left(-\frac{13}{8},-\frac{121}{16}\right)\) at \(x=-\frac{13}{8}\) (ii) \(x=-\frac{13}{8}\)

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