y=-2|x| Will someone please explain how I'm supposed to graph this?
y=-2|-3| was the intended equation
y=-2|x| actually I'm sorry I left some of the details out. It says to let x=-3,-2,-1,0,1,2 and 3. Not sure what to make of this..
|x| simply means "give me the positive result of the number inside"
so |3| = 3
|-3| = 3
I will do the last one, you do the others
y= 2|-2)
= 2(2)
= 4
Certainly! To graph the equation y = -2|x|, we can break it down into two parts - the absolute value function and the negative coefficient.
1. Absolute Value Function: The absolute value of a number returns its distance from zero on the number line. In this case, we take the absolute value of x.
2. Negative Coefficient: The negative coefficient, -2, reflects the graph across the x-axis and flips it upside down.
Now, let's proceed step by step to graph y = -2|x|:
Step 1: Plot the vertex.
- The vertex of the absolute value function |x| is at (0, 0). Therefore, plot a point at the origin.
Step 2: Determine the direction.
- The negative coefficient -2 indicates that the graph will be downward facing or concave down.
Step 3: Plot points on both sides of the vertex.
- Choose some x-values on either side of 0 to evaluate the function and find the corresponding y-values. For example, if we choose x = -2 and x = 2, substitute these values into the equation to find the corresponding y-values.
For x = -2, y = -2|-2| = -2(2) = -4. So, we have the point (-2, -4).
For x = 2, y = -2|2| = -2(2) = -4. So, we have the point (2, -4).
Step 4: Reflect and connect the points.
- Because of the negative coefficient, reflect the points you plotted across the x-axis. In this case, reflect (-2, -4) and (2, -4) to (-2, 4) and (2, 4) respectively.
Step 5: Draw the graph.
- Connect the vertex (0, 0) with the reflected points (-2, 4) and (2, 4) using a smooth curve that goes downward and passes through the vertex.
The final graph of y = -2|x| should be a V-shaped curve, opening downwards, with the vertex at (0, 0) and the legs of the V going through (-2, 4) and (2, 4).