Find the Vertex, the Y-Intercept, and the X-Intercepts (If Any $N ( x ) = 0.15 x ^ { 2 } - 0.25 x + 196.8$

question 112

Multiple Choice

Find the vertex, the y-intercept, and the x-intercepts (if any exist) , and graph the function.
-The number of pets (measured in thousands) living in Springfield homes can be approximated by the equation $N ( x ) = 0.15 x ^ { 2 } - 0.25 x + 196.8$ , where $x$ is the number of years after 1990 . Find $N ( 5 )$ .

• A) \(\mathrm { N } ( 5 ) = 945.55\)
• B) \(\mathrm { N } ( 5 ) = 200,300\)
• C) \(N ( 5 ) = 2500\)
• D) \(\mathrm { N } ( 5 ) = 199,300

---

Definitions:

Therapeutic Alliance

The collaborative and bond between a therapist and a client, which is critical for effective therapy and positive therapeutic outcomes.

Resilience

The capacity to recover quickly from difficulties; emotional strength.

Transference

The projection of feelings, expectations, or desires from one individual onto another, particularly in psychoanalytic contexts.

Cognitive-behavioral Therapies

A group of psychotherapeutic treatments that help patients understand the thoughts and feelings that influence behaviors, commonly used to treat a range of disorders including phobias, addiction, depression, and anxiety.