Question

What is the vertex of the absolute value function defined by ƒ(x) = |x - 2| - 7?

Answer 1

Explanation

• Modulus Function

$y = a |x - h| + k$

The structure or equation is similar to a quadratic function.

The value of a determines the slope of graph.

Tthe value of h determines the horizontal shift of graph.

The value of k determines the vertical shift of the graph.

From the given equation,

$f(x) = |x - 2| - 7$

We can say that the graph shifts to the right 2 units and shifts down 7 units. Hence the vertex would be at x = 2 and y = -7. It can be written in coordinate form as (2,-7).

Answer

$\large{(2,-7)}$