Graph y=a|bx+c|+d with unknown constants: find constants then solve

5. \begin{figure}[h] \end{figure} Figure 2 shows part of the graph with equation \(y = \mathrm { f } ( x )\), where $$\mathrm { f } ( x ) = | k x - 9 | - 2 \quad x \in \mathbb { R }$$ and \(k\) is a positive constant. The graph intersects the \(y\)-axis at the point \(A\) and has a minimum point at \(B\) as shown.

1. 1. Find the \(y\) coordinate of \(A\)
   2. Find, in terms of \(k\), the \(x\) coordinate of \(B\)
2. Find, in terms of \(k\), the range of values of \(x\) that satisfy the inequality $$| k x - 9 | - 2 < 0$$ Given that the line \(y = 3 - 2 x\) intersects the graph \(y = \mathrm { f } ( x )\) at two distinct points,
3. find the range of possible values of \(k\)

3 Fig. 1 shows the graphs of \(y = | x |\) and \(y = a | x + b |\), where \(a\) and \(b\) are constants. The intercepts of \(y = a | x + b |\) with the \(x\)-and \(y\)-axes are \(( - 1,0 )\) and \(\left( 0 , \frac { 1 } { 2 } \right)\) respectively. \begin{figure}[h] \end{figure}

1. Find \(a\) and \(b\).
2. Find the coordinates of the two points of intersection of the graphs.

1 Fig. 1 shows the graphs of \(y = | x |\) and \(y = a | x + b |\), where \(a\) and \(b\) are constants. The intercepts of \(y = a | x + b |\) with the \(x\)-and \(y\)-axes are \(( - 1,0 )\) and \(\left( 0 , \frac { 1 } { 2 } \right)\) respectively. \begin{figure}[h] \end{figure}

1. Find \(a\) and \(b\).
2. Find the coordinates of the two points of intersection of the graphs.