Analyze polynomials in order to sketch their graph.
Log in bdenne14 8 years agoPosted 8 years ago. Direct link to bdenne14's post “How do you match a polyno...” How do you match a polynomial function to a graph without being able to use a graphing calculator? • (18 votes) Stefen 8 years agoPosted 8 years ago. Direct link to Stefen's post “Seeing and being able to ...” Seeing and being able to graph a polynomial is an important skill to help develop your intuition of the general behavior of polynomial function. In practice, we rarely graph them since we can tell a lot about what the graph of a polynomial function will look like just by looking at the polynomial itself. Here is a neat tool where you can change the values of the coefficients of a polynomial and see how it affects the resulting graph - a really great way to develop your "mind's eye" and visualize the graph just by looking at the polynomial. (58 votes) Reginato Rezende Moschen 7 years agoPosted 7 years ago. Direct link to Reginato Rezende Moschen's post “What is multiplicity of a...” What is multiplicity of a root and how do I figure out? • (11 votes) Alissa 6 years agoPosted 6 years ago. Direct link to Alissa's post “When you have a factor th...” When you have a factor that appears more than once, you can raise that factor to the number power at which it appears. For example if you have (x-4)(x+3)(x-4)(x+1) (8 votes) bavila470 6 years agoPosted 6 years ago. Direct link to bavila470's post “Can there be any easier e...” Can there be any easier explanation of the end behavior please. The way that it was explained in the text, made me get a little confused. Also, for the practice problem, when ever x equals zero, does it mean that we only solve the remaining numbers that are not zeros? • (6 votes) MonstersRule 5 years agoPosted 5 years ago. Direct link to MonstersRule's post “This video gives a good e...” This video gives a good explanation of how to find the end behavior: (7 votes) john.cueva 3 years agoPosted 3 years ago. Direct link to john.cueva's post “How can you graph f(x)=x^...” How can you graph f(x)=x^2 + 2x - 5? step by step? • (5 votes) A/V 3 years agoPosted 3 years ago. Direct link to A/V's post “Given a polynomial in tha...” Given a polynomial in that form, the best way to graph it by hand is to use a table. My personal rule is to always use the values most easiest, so let's use -2,-1,0,1,2 F(-2) = (-2)²-2(-2)-5 = 4+4-5 = 3 ==> (-2,3) ^ just a reminder that the number inside the f(x) (e.g f(-1)) is the number that you plug in the equation. As you notice, the value inside the f(x) is the x-coordinate, and the output of that is the y coordinate hopefully that helps ! and if you have any suspicious, 100% recommend using desmos to check your work. (4 votes) Cătălin Gherasim Cîrcu 7 years agoPosted 7 years ago. Direct link to Cătălin Gherasim Cîrcu's post “What throws me off here i...” What throws me off here is the way you gentlemen graphed the Y intercept. Surely there is a reason behind it but for me it is quite unclear why the scale of the y intercept (0,-8) would be the same as (2/3,0). Would appreciate an answer. Have a good day! • (2 votes) Judith Gibson 7 years agoPosted 7 years ago. Direct link to Judith Gibson's post “I see what you mean, but ...” I see what you mean, but keep in mind that although the scale used on the X-axis is almost always the same as the scale used on the Y-axis, they do not HAVE TO BE the same. (7 votes) manasvi 10 months agoPosted 10 months ago. Direct link to manasvi's post “How do you find the end b...” How do you find the end behavior of your graph by just looking at the equation. how do you determine if it is to be flipped? • (3 votes) noedig101 10 months agoPosted 10 months ago. Direct link to noedig101's post “by looking at the highest...” by looking at the highest degree term. combine the two to figure out negative infinity. (4 votes) Coward 3 years agoPosted 3 years ago. Direct link to Coward's post “Question number 2--'which...” Question number 2--'which of the following could be a graph for y = (2-x)(x+1)^2' confuses me slightly. Shouldn't the y-intercept be -2? • (3 votes) Kim Seidel 3 years agoPosted 3 years ago. Direct link to Kim Seidel's post “You have a math error. 2-...” You have a math error. 2-0 = 2, not -2. (3 votes) meet05 5 years agoPosted 5 years ago. Direct link to meet05's post “You should put a practice...” You should put a practice for this topic • (4 votes) StudyBuddy a year agoPosted a year ago. Direct link to StudyBuddy's post “Hi! Here's a tip for find...” Hi! Here's a tip for finding the y-coordinate of the y-intercept without rewriting the factored form in standard form. Multiply all the constant parts of the factors. So if you have (x+1)(x-2)(x+5), you multiply(1)(-2)(5) = -10. And that's the y-coordinate of the y-intercept! Check it out! And do let me know if this helped anyone by upvoting or leaving a comment. :) • (3 votes) David Severin a year agoPosted a year ago. Direct link to David Severin's post “That makes sense because ...” That makes sense because the y intercept is where x=0, so you just set x=0 in this case. (2 votes) noedig101 10 months agoPosted 10 months ago. Direct link to noedig101's post “where are the exercises f...” where are the exercises for this? • (3 votes) Angad 8 months agoPosted 8 months ago. Direct link to Angad's post “Sadly, I believe there ar...” Sadly, I believe there are none. (2 votes)Want to join the conversation?
For example, given ax² + bx + c
If a is positive, the graph will be like a U and have a minimum value.
If a is negative, the graph will be flipped and have a maximum value
If |a| is > 1 the parabola will be very narrow.
If |a| is < 1 the parabola will be very wide.
The axis of symmetry (and the location of the vertex) is given by -b/2a.
When you factor the function, you get the x-intercepts (if any).
When you set x=0 you get the y intercept of the graph (if any).
Check out these pages for more information:
https://www.mathsisfun.com/algebra/quadratic-equation-graphing.html
https://www.mathsisfun.com/algebra/quadratic-equation-graph.html
the multiplicities of each factor would be:
x-4= multiplicity 2
x+3+ multiplicity 1
x+1= Multiplicity 1
https://www.khanacademy.org/math/algebra2/polynomial-functions/polynomial-end-behavior/v/polynomial-end-behavior
(I'm new here)
F(-1) = (-1)²-2(-1)-5 = 1+2-5 = -2 ==> (-1,-2)
F(0) = (0)² -2(0) -5 = 0-0-5 = -5 ==> (0,-5)
F(1) = (1)² -2(1) -5 = 1-2-5 ==> (1,-6)
F(2) = (2)² -2(2)-5 = 4-4-5 = (2,-5)
(e.g (-1,-2) at f(-1)).
I can't answer for the designers of the graph, but perhaps they wanted to save space, or perhaps it was done in error --- who knows!
kx^n
if n is even, the two "ends" will be the same. if it's odd they will be different.
k determines what infinity is.
if k is positive, infinity will be positive.
if k is negative, infinity will be negative.
y = (2-0)(0+1)(0+1)
y = (-2)(1)(1)
y = -2
What makes the y-intercept positive 2 instead of negative 2?
So, the y-intercept is at y=+2
