Question

Vertex for 1/2 |x+3|+1

Answer 1

The vertex of the function 1/2 |x+3| + 1 is found by setting the expression within the absolute value to zero, resulting in x = -3. Substituting this back into the function gives the y-coordinate of 1, making the vertex of the function (-3, 1).

Step-by-step explanation:

The student is asking about the vertex of the function 1/2 |x+3| + 1.

The vertex of an absolute value function like this is the point at which the function changes direction, which occurs at the 'turning point' within the absolute value.

Since the absolute value expression is |x+3|, the function changes direction when x+3 is equal to zero, which occurs when x = -3. Substituting x = -3 into the function gives the y-coordinate of the vertex:

1. Set the expression inside the absolute value to zero: x+3 = 0.
2. Solve for x: x = -3.
3. Find the y-coordinate by substituting x into the function: 1/2 |(-3)+3| + 1 = 1/2 |0| + 1 = 1.
4. The vertex of the function is therefore at the point (-3, 1)