High School Math : Graphing Absolute Value

Study concepts, example questions & explanations for High School Math

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Example Questions

Example Question #4 : Absolute Value

Find the \(\displaystyle x\)-intercepts for the graph given by the equation:

\(\displaystyle y=\left | 2x-6\right |-8\)

Possible Answers:

\(\displaystyle x=-1\ and\ 1\)

\(\displaystyle x=-7\ and\ 1\)

\(\displaystyle x=-1\ and\ 7\)

\(\displaystyle x=1\ and\ 7\)

\(\displaystyle x=-7\ and\ 1\)

Correct answer:

\(\displaystyle x=-1\ and\ 7\)

Explanation:

To find the \(\displaystyle x\)-intercepts, we must set \(\displaystyle y=0\).

To solve absolute value equations, we must understand that the absoute value function makes a value positive. So when we are solving these problems, we must consider two scenarios, one where the value is positive and one where the value is negative.

\(\displaystyle y=\left | 2x-6\right |-8\)

\(\displaystyle 0=\left | 2x-6\right |-8\)

\(\displaystyle \left | 2x-6\right |=8\)

Now we must set up our two scenarios:

\(\displaystyle 2x-6=8\) and \(\displaystyle 2x-6=-8\)

\(\displaystyle 2x=14\) and \(\displaystyle 2x=-2\)

\(\displaystyle x=7\) and \(\displaystyle x=-1\)

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