Question

Identify the vertex, intercepts and whether of the graph of the function below opens up or down. Type your answers as a point (x,y). If an intercept does not exist type "none". If more than one intercept exists you can type either intercept.f(x)= -|x-1|-2 Vertex = Answerx intercept = Answery intercept = Answergraph opens Answer

Answer 1

Answer:

Vertex = (1, -2)

x - intercept = None

y-intercept = (0, -3)

Graph opens down

Step-by-step explanation:

The given absolute value function is:

f(x) = -|x - 1| - 2

Generally, an absolute value function is of the form:

f(x) = a|x - h| + k

where the vertex is (h, k)

Comparing the given function with the general absolute value function:

a = -1, h = 1, k = -2

Therefore, the vertex, (h, k) = (1, -2)

To find the x-intercept, substitute f(x) = 0 into the function

0 = -|x - 1| - 2

-|x - 1| = 2

|x - 1| = -2

There are no real roots for this equation. Therefore, there is no x-intercept

The x-intercept = None

To find the y-intercept, substitute x = 0 into the function

f(x) = -|0 - 1| - 2

f(x) = -|-1| - 2

f(x) = -1 - 2

f(x) = -3

The y-intercept = (0, -3)

Since a = -1 (that is, negative), the graph opens down