Question

use technology to find points and then graph the function $y = -2|x| + 5$, following the instructions below.
done plotting points
plot at least five points that fit on the axes below. click a point to delete it.

Explanation:

Step1: Choose x - values

We can choose x - values such as \(x=-2\), \(x = - 1\), \(x=0\), \(x = 1\), \(x=2\) to find the corresponding y - values.

Step2: Calculate y for \(x=-2\)

Substitute \(x=-2\) into \(y=-2|x| + 5\). Since \(|x|=|-2| = 2\), then \(y=-2\times2 + 5=-4 + 5 = 1\). So the point is \((-2,1)\).

Step3: Calculate y for \(x=-1\)

Substitute \(x = - 1\) into \(y=-2|x|+5\). Since \(|x|=|-1| = 1\), then \(y=-2\times1+5=-2 + 5=3\). So the point is \((-1,3)\).

Step4: Calculate y for \(x = 0\)

Substitute \(x=0\) into \(y=-2|x|+5\). Since \(|x|=|0| = 0\), then \(y=-2\times0 + 5=5\). So the point is \((0,5)\).

Step5: Calculate y for \(x = 1\)

Substitute \(x = 1\) into \(y=-2|x|+5\). Since \(|x|=|1| = 1\), then \(y=-2\times1+5=-2 + 5 = 3\). So the point is \((1,3)\).

Step6: Calculate y for \(x=2\)

Substitute \(x = 2\) into \(y=-2|x|+5\). Since \(|x|=|2| = 2\), then \(y=-2\times2+5=-4 + 5=1\). So the point is \((2,1)\).

To graph the function, we plot the points \((-2,1)\), \((-1,3)\), \((0,5)\), \((1,3)\), \((2,1)\) (and we could also choose other x - values like \(x = 3\), where \(y=-2\times3 + 5=-1\), point \((3,-1)\) or \(x=-3\), \(y=-2\times3+5=-1\), point \((-3,-1)\) if we want more points). After plotting the points, we can see that the graph of \(y=-2|x| + 5\) is a V - shaped graph (absolute value function) opening downwards with vertex at \((0,5)\).

Answer:

The five points are \((-2,1)\), \((-1,3)\), \((0,5)\), \((1,3)\), \((2,1)\) (you can plot these points on the given coordinate system to graph the function \(y=-2|x|+5\)).