Solve the following inequality algebraically. ∣x−5∣≤11

Step-by-step explanation:

So we have the inequality:

Definition of Absolute Value:

Note that the sign is flipped in the second case because we multiplied by a negative.

Add 5 to both sides to both equations:

Merge:

And we're done!

Remember that the vertex form of a parabola is where is the vertex of the parabola.

Now, to find the vertex of the parabola, we are going to use the vertex formula:

For a quadratic of the form , the vertex is given by:

in other words, we find by evaluating the function at

We know form our quadratic that and , so let's use our formula to find :

Now we can evaluate our function at to find :

Now, we can rewrite our parabola in vertex form:

, , and

We can conclude that the correct answer is: y = 6(x + 1)2 – 16