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Zeros of polynomials: matching equation to graph

When we are given the graph of a polynomial, we can deduce what its zeros are, which helps us determine a few factors the polynomial's equation must include.

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• how does the point: 1.5 make 3/2?
• 1.5 = 1.5/1 = 15/10 = 3/2
decimal and fraction equivalents
• How do you know whether the graph is upwards opening or downward opening, could you multiply the binomials, and then simplify it to find it?
• Typically when given only zeroes and you want to find the equation through those zeroes, you don't need to worry about the specifics of the graph itself — as long as you match it's zeroes.

However, if you want to graph the equation at it's entirety, the best way (imo, if someone else has a better option please leave down in the replies/comments for him), is to simply multiply it out.

* It is best to know that if it's a quadratic equation (degree is 2), just find whether or not a is positive or negative, open up or down at it's respective order.

* If it's a cubic or higher , it's better to refer to demos or graph by hand as there are multiple phases that the graph could potentially open up or down.

hopefully that helps !
• I was wondering how this will be useful in real life. Does anyone have a good solution?
• Obviously, once you get to math at this stage, only a few jobs use them. I guess that since polynomials can make curves when put on a graph, it can be used for construction planning.
• Is the concept of zeros of polynomials: matching equation to graph the same idea as the concept of the rational zero theorem?
• The concept of zeroes of polynomials is to solve the equation, whether by graphing, using the polynomial theorem, graphing, etc.
• what does p(x) mean
• That refers to the output of functions p, just like f(x) is the output of function f. Function p takes in an input of x, and then does something to it to create p(x). Functions can be called all sorts of names.
• I don't understand where the Y comes from? aren't we dealing with polynomials with the variable x ? why is y = p(x)
• P(x) or more commonly symbolized as F(x) simply represents the y-value at a given point. When finding the "zeros" or "x-intercepts" of a function/graph you are trying to find the values that would result in each factor equaling zero resulting in the entire equation being equal to zero. Lets use some of the factors from the video (x+4) and (x-3), when you set these factors separately equal to zero x+4=0 and x-3=0 and solve, you find that the x values must be equal to -4 and 3 respectively, which means at those x-values on the graph the equation/ p(x) will be equal to zero or the Y-VALUE will be equal to zero. This is true for each factor.

p(x)=(x+4)(x-3)
p(x)=(-4+4)(x-3)
p(x)=(0)*(x-3)
p(x)=0
y=0

p(x)=(x+4)(x-3)
p(x)=(x+4)(3-3)
p(x)=(x+4)*(0)
p(x)=0
y=0

Hope this helps!
• how did u get 3/2
• Quite simple acutally. If you take a look, when the line intercepts the x axis, there is: -4, 1.5, and 3. Sal said 3/2 instead of 1.5 because 1.5 in fraction form is 3/2.
(1 vote)
• What I've Learned

-The determination of the zeros of a polynomial graph is a crucial step in discerning the factors that must be included in the polynomial's equation. By analyzing the points at which the graph intersects the x-axis, we can ascertain the roots of the polynomial, which, in turn, aid in identifying the key features of the function.
• Hi!

Quick Q, isn't B correct as well? Or is it that since D had more solutions - that is the correct answer?

**I did solve for B, although I did with only -4 and 3 but didn't account the 3/2 that Sir had found but is it still correct?
(1 vote)
• The equation must satisfy all the zeroes.