Equations & Graphs of a Polynomial Function (going mumbo jumbo)

Oh my goddddddddddddddddddddddddddddddddddddddd!!! This isn't as easy as I expected! Especially with the textbook answers all different from Darren's. Sh*t.....what's going onnn...?? The more I look at those unanswered questions, the more I go mumbo jumbo up in my head. I REALLY do get the concept. But what is up with those weird questions answers? =(

Nevermind. Let's get the concet straight first!

Given the polynomial function

y = x² + 1

   = (x + 1)(x – 1)

Solely from an equation, this is the information you need to spot in order to sketch the function's graph without using a graphing calculator.

i) The sum of exponents of all factors (the equation has 2 factors with an exponent of 1. Thus, The sum of exponents of the equation is 2. note: each bracket is a factor.)

ii) The sign in front of the product of all x's (x x x = x² . Therefore, we can see that the sign in front of the product of all x's in the function is a positive sign)

iii) The x-intercept and y-intercept of the function (substitute y = 0 to get x-intercept and x = 0 to get y-intercept)

iv) The positive/negative sign of f(x) (substitute an x value to determine if f(x) is positive or negative at that particular x point)

 

Similarly, from a given graph, you will be able to identify and state the

i) Degree = 2 ; because it has n x-intercept, n - 1 local maximum/minimum point and its graph extends from quadrant 2 to quadrant 1. This information is enough to show that the graph has an even degree of 2 =D

ii) Sign of leading coefficient = Positive ; because the graph extends from quadrant 2 to quadrant 1

iii) x-intercept = -1, 1

      y-intercept = -1

iv)

Intervals	x < -1	-1 < x < 1	x > 1
Sign of f(x)	+	-	+

The new phrase of the day!

...has a zero at x = ? with order of ?...

Ok Ok...calm down. Read more, you'll understand better.

Let's say... y = -2 (x – 3)²

Expand it,    x - 3 = 0

                    x = 3

Hence, the function has a zero at x = 3 with the order of 2

Not too difficult right? The term "with the order of" is basically just the highest power of the function

Ps: I found this site where this person posted a quartic function question and there were many comments posted there. I think the comments, explanations and answers really help. Click Here

Alright then...not-too-happy-math! Till I solve more questions!