Expert: Paul Klarreich - 11/24/2011

Question
Part of the graph of f(x)=(x-p)(x-q) is shown below.[in pic attached].
The Vertex is at C. The graph crosses the y-axis at B.

(a) write down the value of p and q?
(b) find the coordinates of C?
(c) Write down the y-coordinate of B?

Answer
Questioner: kevin
Country: Beijing, China
Category: Calculus
Private: No
Subject: calculus
Question:

Part of the graph of f(x)=(x-p)(x-q) is shown below.[in pic attached].
The Vertex is at C. The graph crosses the y-axis at B.

(a) write down the value of p and q?
(b) find the coordinates of C?
(c) Write down the y-coordinate of B?  
..............................................
Use these facts and definitions:

A. a ZERO of f(x) is a value of x that makes f(x) = 0.

B. a ZERO of f(x) is a value of x at a crossing of the x-axis.

C. (The Factor Theorem)  If  f(a) = 0,  then  (x - a) is a factor of f(x).

Put those facts together for your (a).  You will know f(x).  Then try to answer (c).

[Your graph is not good enough to answer (b).]

P.S. Your questions belong in the ADVANCED MATH section, not calculus.