Sketch the graph of $y=\left| 2{{x}^{2}}-7x-4 \right|$ for $-2\le x\le 5$, indicating clearly th

Question

Sketch the graph of $y=\left| 2{{x}^{2}}-7x-4 \right|$ for $-2\le x\le 5$, indicating clearly the coordinates of the end-points, intercepts and turning point. Hence, write down the value of $k$ for which the equation $\left| 2{{x}^{2}}-7x-4 \right|=k$ has exactly $3$ solutions for $-2\le x\le 5$.

Accepted Answer

Endpoints $(-2,18),(5,11)$; intercepts $(-\frac12,0),(4,0),(0,4)$; central turning point $(\frac74,\frac{81}8)$; $k=\frac{81}8$.

Modulus Function - Graphs of Modulus Function

Modulus Function - Graphs of Modulus Function

Solution:

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