<p>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.</p>
<ol class="i-list"><li><div class="list-item-paragraph">Find the value of $k$ and of $m$.</div></li><li><div class="list-item-paragraph">Hence find the coordinates of $A$, $B$and $C$.</div></li><li><div class="list-item-paragraph">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.</div></li></ol>
<figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/public/question-images/pasted/1766032910829-q3lnjjsawld.png" style="max-width: 300px; height: auto; display: block;" class="aligncenter custom-width" /></figure>

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.

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.

Modulus Function - Graphs of Modulus Function

Modulus Function - Graphs of Modulus Function