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How to find the vertex of an absolute value function?

a) Use the formula -b/(2a)
b) Set the inside expression equal to zero
c) Complete the square
d) Take the absolute value of the coefficient of x

User Zeytin
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1 Answer

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Final answer:

To find the vertex of an absolute value function, set the inside expression equal to zero to find the x-coordinate and substitute it back into the function to find the y-coordinate. The correct answer is b) Set the inside expression equal to zero.

Step-by-step explanation:

To find the vertex of an absolute value function, you can use the formula -b/(2a) from the options provided. The vertex form of an absolute value function is f(x) = a|x - h| + k, where (h, k) represents the vertex of the graph. In this form, the value of h is obtained by setting the inside expression equal to zero.

So, out of the given options, b) Set the inside expression equal to zero is the correct way to find the x-coordinate of the vertex. Let's go through an example:

Example:

Consider the absolute value function f(x) = |x + 2| + 3. To find the vertex, set the inside expression, x + 2, equal to zero: x + 2 = 0. Solving this equation gives x = -2. So the x-coordinate of the vertex is -2.

To find the y-coordinate, substitute this value back into the function: f(-2) = |-2 + 2| + 3 = 3. Therefore, the vertex of the absolute value function is (-2, 3).

User JuggernautDad
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