Question

This is confusing. Please help.

List the zeros, degrees, and end behavior of each functions. Then draw a general sketch of the function.

1. y = (x+3)(x-2)
2. y = -(x+2)(x-4)

Answer 1

To find the zeros of a function, you set y = 0 and solve for x :)
Degree of a function is the largest exponent (power) of the variable... So for e.g.
\[y = x^4 + 2x - 7\] the degree would be 4.

Answer 2

So for #1, the degree would be 2?

Answer 3

yes! :)

Answer 4

Oh, okay. Thank you!

Answer 5

no problemo :D

Answer 6

Do you know how to find the end behavior and sketch ?

Answer 7

Uh, lol not really sure

Answer 8

okay, so the end behaviour is basically just asking which way the ends of the function is facing...So i'll use an example.
If we had the function y = ( x - 4 ) ( x + 2 )
and they wanted me to list the zeros, degrees and end behaviour and sketch i would firstly do this:
Set y = 0 to find the ZEROS

0 = ( x - 4 ) ( x + 2 )
This means that x - 4 = 0 or x + 2 = 0
Therefore x = 4 or -2 right?

Next, just by looking at the function.. you should be able to tell that it is a quadratic function (so the highest degree would be 2 bc x^2).

Then if we look at the function y = (x - 4) (x + 2), if i EXPAND this it will become:
y = x^2 + 2x - 4x - 8
y = x^2 - 2x - 8
and since x^2 is POSITIVE (so it isn't -x^2), i know this means that the sketch will be a "happy face sketch" meaning that the ends will both be increasing:

See how when x = -2 , y = 0 and when x = 4, y = 0 (you can think of these as your x-intercepts) and these points will show you where the graph will cut the x-axis.
If you look at the arrow heads (ends of the graph) can you see how both are going upwards? this is because of the POSITIVE x^2 :)
hope this helps