Example: f(x)= 2x^3 + 3x^2 - 8 + 3
Step 1: find all possible roots..
p: factors of 3: 1, -1, 3, -3
q: factors of 2: 1, -1, 2, -2
*p is the leading constant term & q is the leading coefficient
possible roots are (p/q): 1, -1, 1/2, -1/2, 3, -3, 3/2, -3/2
Step 2: now you can plug all of the possible roots in your calculator to find the roots that work
- the zero will be: 1, 1/2, -3
you should get: (x - 1) (2x^2 + 5x + 3)
Step 4: slove further
(this can be factored...)
= (x - 1) (2x^2 + 5x + 3)
= (x - 1) (2x - 1) (x + 3)
(set x = 0 )
x = 1, 1/2, -3
Sketching polynomials functions is something I need help with. I really don't understand how to plug all of that in my calculator. If someone can help me with that...that would be great.
thanx amy i now understand where i went wrong on my explanation
ReplyDeleteoh and one more thing amy. when you are finding your p's, you had like terms that could be put together. -8 and 3 should have been combined into -5, which makes your p's +/-1, +/-5
ReplyDeleteSketching polynomial functions is real easy. All you have to do is basically connect the dots in a squiggly line. And you have to figure out if it starts going down or up. Once you get all of your f(x)'s, you figure out if your first f(x) is positive or negative. If its negative it starts below the x-axis; if its positive it starts above the x-axis. Now if your only problem is plugging it in then its real simple.
ReplyDeleteAll you have to do is press Y= on your calculator. Then you plug in the formula exactly how you see it. Then press graph and it will graph itself.
oh weber, why do you always find something wrong with my posts?..lol..jk..thank you..i see what ya mean...
ReplyDeleteand thank you cupit..i think i get it now..
1st. factor the problem completely
ReplyDelete2nd. draw your number line and label your roots
3rd. plug in (from both sides of every root) into your origional eqn to find your -ve's and +ve's going from least to greatest
4th. draw your graph and plant your coordinates
5th. look at your first +/-ve to decide whether to start up or down
6th. draw your squiggle (connect the dots) in acordance with your +/-ve's
NOW YOU'VE GOT YOUR GRAPH
and you just have to find your maximum and minimum.
all you have to do is:
ReplyDelete1st- press y= then type in your equation
2nd- press graph snd it should graph your parabola.