QuestionWhat is the vertex of the following function? $y=2|x-3|+1$

Studdy Solution

STEP 1

1. The function is in the form of a vertical stretch and translation of the absolute value function.
2. The vertex form of an absolute value function is $y = a|x-h| + k$ , where $(h, k)$ is the vertex.

STEP 2

1. Identify the form of the absolute value function.
2. Determine the vertex from the function's equation.

STEP 3

The given function is $y = 2|x-3| + 1$ .
This matches the vertex form $y = a|x-h| + k$ .

STEP 4

From the equation $y = 2|x-3| + 1$ , identify $h$ and $k$ .
Here, $h = 3$ and $k = 1$ .
The vertex of the function is $(h, k) = (3, 1)$ .
The vertex of the function is:
$\boxed{(3, 1)}$

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