# How do you graph #y=2abs(x+6)-10#?

See the explanation

The bit inside the | | can be positive or negative but writing it like

At

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See the Socratic graph and explanation.

The equation represents the point of intersection #V(-6, -10) and the

V-part of the two lines above

Proof using algebra:

It inserts the Socratic graph.

diagram{2|x+6|-10 [-20, 20, -11, 9]}

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To graph the equation ( y = 2| x + 6 | - 10 ), you first need to understand the shape of the absolute value function. The absolute value function ( |x| ) has a "V" shape with its vertex at the origin. When you add or subtract values inside the absolute value function, it shifts the graph horizontally.

For the equation ( y = 2| x + 6 | - 10 ), the graph will shift the graph of ( y = 2| x | ) horizontally 6 units to the left and vertically 10 units down.

So, the vertex of the graph will be at the point ((-6, -10)), and the shape will be a "V" opening upwards.

You can then plot additional points to sketch the graph, or use the knowledge that the graph is symmetric to complete the sketch.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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