Sketch of x^3-2x^2+5 using synthetic division

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In summary, the conversation discusses finding the sketch of the function f(x)=x^3-2x^2+5 using synthetic division to simplify it. It also mentions finding factors and points on the x and y axes, and determining turning points. However, it is later realized that a sketch can be approximated without finding the intercepts.
  • #1
St@rbury
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Homework Statement


sketch f(x)=x^3-2x^2+5


Homework Equations


none


The Attempt at a Solution


i tried to uses synthetic division to bring it down to a lower power, but i can't remember what to do because i don't know any of the factors...
 
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  • #2
Well first you would try to find factors such that f(a)=0, if f(a)=0 then (x-a) is a factor of f(x).

Seeing as how the last number there is 5, then you should try,1,-1,-5,5 and see if any are zero.

If you do not find it to be zero,then either it has complex roots or non-integer roots.
find where it cuts the f(x)-axis and x-axis. Find turning points(and whether they are max or min points) and try to sketch. If you need more help, reply back
 
  • #3
it didnt work... and seeing as this was a homework question i don't think my teacher would have made it so complex...did i set up the synthetic division correctly?

5 | 1 -2 0 5
________
________
 
  • #4
yea...i set it up right..turns out that i didnt need to find the intercepts, and couldve just aproximated a sketch
 

Related to Sketch of x^3-2x^2+5 using synthetic division

1. What is the domain of the function?

The domain of the function is all real numbers since there are no restrictions on the possible values of x in the equation.

2. What is the range of the function?

The range of the function is also all real numbers, since the function is a polynomial and has no limitations on the possible outputs.

3. What are the x-intercepts of the function?

To find the x-intercepts, we set y=0 and solve for x. In this case, the x-intercepts are (0,0) and (5,0).

4. What are the critical points of the function?

The critical points of a function are where the derivative is equal to 0 or does not exist. In this case, the critical points are x=0 and x=5.

5. How does the graph of the function change if the coefficient of x^3 is multiplied by a negative number?

If the coefficient of x^3 is multiplied by a negative number, the graph of the function will be reflected about the x-axis. This means that the positive and negative values of the function will switch, but the overall shape of the graph will remain the same.

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