Question

graph this function:
y = 5|x| - 7
click to plot the vertex first.
(graph with x-axis from -10 to 10 and y-axis from -10 to 10, grid lines, and axes labeled. submit button and work it out link at bottom.)

Explanation:

Step1: Identify vertex form

The absolute - value function is in the form \(y = a|x - h|+k\), where \((h,k)\) is the vertex. For the function \(y = 5|x|-7\), we can rewrite it as \(y=5|x - 0|-7\). So, \(h = 0\) and \(k=-7\).

Step2: Plot the vertex

The vertex of the function \(y = 5|x|-7\) is at the point \((0,-7)\). On the given coordinate grid, we find the point where \(x = 0\) and \(y=-7\) and plot it.

Step3: Find other points

We can find two more points to draw the graph. For \(x = 1\), \(y=5|1|-7=5 - 7=-2\). For \(x=- 1\), \(y = 5|-1|-7=5 - 7=-2\). We can also use \(x = 2\), \(y=5|2|-7 = 10 - 7 = 3\) and \(x=-2\), \(y=5|-2|-7=10 - 7 = 3\). After plotting the vertex and these points, we can draw the V - shaped graph of the absolute - value function. But the first step is to plot the vertex \((0,-7)\).

Answer:

The vertex of the function \(y = 5|x|-7\) is at the point \((0,-7)\), so we plot the point \((0,-7)\) on the graph.