Question

graph this function:
y = |x| + 2
click to plot the vertex first.
(graph with x-axis from -10 to 10 and y-axis from -10 to 10, grid lines, and a submit button at the bottom.)

Explanation:

Step1: Identify the vertex of the absolute - value function

The general form of an absolute - value function is \(y = |x - h|+k\), where \((h,k)\) is the vertex of the V - shaped graph. For the function \(y=|x| + 2\), we can rewrite it as \(y=|x - 0|+2\). So, by comparing with the general form, we find that \(h = 0\) and \(k = 2\). This means the vertex of the graph of the function \(y = |x|+2\) is at the point \((0,2)\).

Step2: Plot the vertex

On the given coordinate grid, we locate the point \((0,2)\). The \(x\) - coordinate is \(0\) (which is on the \(y\) - axis) and the \(y\) - coordinate is \(2\). So we click on the point \((0,2)\) to plot the vertex. After plotting the vertex, we can find other points to complete the graph. For example, when \(x = 1\), \(y=|1| + 2=1 + 2 = 3\), so the point \((1,3)\) is on the graph. When \(x=- 1\), \(y=|-1|+2 = 1 + 2=3\), so the point \((-1,3)\) is on the graph. We can use these points (and more) to draw the V - shaped graph of the absolute - value function. But the first step is to plot the vertex at \((0,2)\).

Answer:

The vertex of the function \(y = |x|+2\) is at the point \((0,2)\), so we plot the point \((0,2)\) on the graph.