Question

y = -5|x|
click to plot the vertex first.

Explanation:

Step1: Identify the vertex of the absolute - value function

The general form of an absolute - value function is \(y = a|x - h|+k\), where \((h,k)\) is the vertex of the function. For the function \(y=-5|x|\), we can rewrite it as \(y = - 5|x - 0|+0\). So, the vertex \((h,k)\) is \((0,0)\). We plot the point \((0,0)\) on the coordinate plane.

Step2: Find another point on the function

Let's choose a value for \(x\), say \(x = 1\). Substitute \(x = 1\) into the function \(y=-5|x|\). We know that \(|1|=1\), so \(y=-5\times1=-5\). So, the point \((1, - 5)\) is on the function. Similarly, if we choose \(x=-1\), \(| - 1| = 1\), and \(y=-5\times1=-5\), so the point \((-1,-5)\) is also on the function. We can plot these points and then draw the graph of the V - shaped absolute - value function. The graph opens downwards because the coefficient of \(|x|\) (\(a=-5\)) is negative, and it is vertically stretched by a factor of 5.

Answer:

The vertex is at \((0,0)\), and other points like \((1, - 5)\) and \((-1,-5)\) can be used to plot the graph of \(y = - 5|x|\). The graph is a V - shaped graph opening downwards with vertex at the origin and passing through \((1, - 5)\) and \((-1,-5)\) (and other similar points).