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Math  /  Algebra

Question21/23
What is the equation of the absolute value function with a vertex at (1,−2)(1,-2) ? ∣x−1∣−2|x-1|-2 f(x)=∣x+1∣+2f(x)=|x+1|+2 f(x)=∣x−1∣+2f(x)=|x-1|+2 f(x)=f(x)=

Studdy Solution

STEP 1

1. The absolute value function has the form f(x)=∣x−h∣+k f(x) = |x - h| + k , where (h,k)(h, k) is the vertex of the function.
2. The vertex of the function is given as (1,−2)(1, -2).

STEP 2

1. Identify the vertex form of the absolute value function.
2. Substitute the vertex coordinates into the vertex form.
3. Write the equation of the absolute value function.

STEP 3

Identify the vertex form of the absolute value function. The general form of an absolute value function is:
f(x)=∣x−h∣+k f(x) = |x - h| + k
where (h,k)(h, k) is the vertex of the function.

STEP 4

Substitute the vertex coordinates (1,−2)(1, -2) into the vertex form. Replace hh with 1 and kk with -2:
f(x)=∣x−1∣−2 f(x) = |x - 1| - 2

STEP 5

Write the equation of the absolute value function using the substituted values:
The equation of the absolute value function is:
f(x)=∣x−1∣−2 f(x) = |x - 1| - 2
The equation of the absolute value function with a vertex at (1,−2)(1, -2) is f(x)=∣x−1∣−2 f(x) = |x - 1| - 2 .

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