The diagram shows the graph of $y=\left| k-2x \right|+m$, where $k$ and $m$ are integers.

Question

The diagram shows the graph of $y=\left| k-2x \right|+m$, where $k$ and $m$ are integers. $A$ is the point where the graph intersects the $y$-axis, and $B$ and $C$ are the points where it intersects the $x$-axis. Point $D\left( 3,-2 \right)$ is the vertex of the graph. Find the value of $k$ and of $m$. Hence find the coordinates of $A$, $B$ and $C$. Using the graph, write down the range of values of $p$, such that the equation $px=\left| k-2x \right|+m$ has 2 distinct solutions.

Accepted Answer

(i) $k=6,m=-2$. (ii) $A=(0,4),B=(2,0),C=(4,0)$. (iii) $-\frac23<p<2$.

Modulus Function - Graphs of Modulus Function

Modulus Function - Graphs of Modulus Function

Solution:

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