Find The Equation Of A Cubic Relationship Given This Data

In summary, the conversation involved finding the equation of a cubic relationship with specific points and intercepts. The solution involved factoring and solving for the unknown variables. The second part of the conversation discussed finding the turning points of the equation. While using calculus was suggested, it was also mentioned that a graphical calculator could be used. The conversation also involved some confusion about the use of point-slope formulas and the level of mathematics involved.
  • #1
1. Find the equation of a cubic relationship given that the graph has only two x intercepts, one at point (3,0) and the other at (-1,0). It is also known that the graph passes through the point (4,-10) and has a y-intercept of (0,-18)

2. Write down the exact co-ordinates of the two turning points of the equation found in question 1.
 
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  • #2
So, what thoughts have you had on this problem?
 
  • #3
drunkenfool said:
1. Find the equation of a cubic relationship given that the graph has only two x intercepts, one at point (3,0) and the other at (-1,0). It is also known that the graph passes through the point (4,-10) and has a y-intercept of (0,-18)

2. Write down the exact co-ordinates of the two turning points of the equation found in question 1.

first y = k(x-3)(x+1)(x-q)
q has to be 3 or -1 since the graph only touches one of these points.
and k*(-3)*1*(-q)=-18
so k = -6/q
subsitute into first equation and become
y = -6/q(x-3)(x+1)(x-q)
and it pass through the point 4, -10
then it becomes
-10 = -6/q(4-3)(4+1)(4-q)
solve for q
q=3
k = -2



2. turning point?? means inflection point or extrema? but since it said 2 turning points... i guess it means extrema. first, take first derivative and then find zero. that is your extrema.(turning point)?
x @ 1/3, 3 ?
 
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  • #4
my thoughts were: y=a(x-3)(x+1)(x+k) and i was kinda stuck as..
thanks for d speedy help and uve made it understandable thanks.

so the answer to (a) is: y= -2(x-3)(x-3)(x+1)
i get it now great..

but then B? use graphical calc
 
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  • #5
am i right on part b?
 
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  • #6
drunkenfool said:
am i right on part b?
My calcultor gives the same result. If you are taking calculus, you can approach this problem by taking the dirivative of the function you found in part a), setting it equal to zero, and solving the quadratic equation for x. If you are not taking calculus, that will not mean anything to you and the calculator solution is probably what is expected of you.
 
  • #7
wow I am so good
 
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  • #8
Find The Equation Of A Cubic Relationship Given This Data?

Does this math Have to do with Point-Slope fomulas. Slope=Rise/Run.
Ifso,then I have the anser of how to solve it, for you. If, you want to know the anser , then just let me know.

I'm Hear to help in any way possable. "THANK YOU"

With many Smiles,
Lil`SciWizGirl.
 
  • #9
Nope,no point slopes here.Just some well done factoring and simple algebra.

Daniel.
 
  • #10
Lil`SciWizGirl said:
Find The Equation Of A Cubic Relationship Given This Data?

Does this math Have to do with Point-Slope fomulas. Slope=Rise/Run.
Ifso,then I have the anser of how to solve it, for you. If, you want to know the anser , then just let me know.

I'm Hear to help in any way possable. "THANK YOU"

With many Smiles,
Lil`SciWizGirl.

The easier way to solve slope problem is calculus...
but i believe he is not in calculus, and point-slope formula means nothing if we don't know the actually point and slope.
 
  • #11
yea this isjust normal yr 11 maths..acually i think i got part b right as well so yer thnx older dan. and thanks for all the other help esp leon1127. anyway the assignments handed in and over. thanks
 

1. How do you identify a cubic relationship from a set of data?

A cubic relationship can be identified by plotting the data points on a graph and observing a curve that resembles the shape of a "cubic" or "cube" (a three-dimensional square). This curve will have a steep increase, followed by a gradual decrease or leveling off.

2. What is the general form of a cubic equation?

The general form of a cubic equation is y = ax^3 + bx^2 + cx + d, where a, b, c, and d are constants and x is the independent variable. This equation represents a curve with a degree of 3, which is characteristic of a cubic relationship.

3. How many data points are needed to find the equation of a cubic relationship?

To determine the equation of a cubic relationship, at least four data points are needed. This is because a cubic equation has four unknown constants (a, b, c, and d) that can be solved using four data points.

4. Can a cubic equation be used to predict future data points?

Yes, a cubic equation can be used to predict future data points, but the accuracy of the prediction may depend on the quality and quantity of the data used to create the equation.

5. How do you solve for the constants in a cubic equation?

To solve for the constants in a cubic equation, you can use a variety of methods such as substitution, elimination, or graphical methods. The most common method is to use a process called "least squares regression" which involves minimizing the sum of the squared differences between the data points and the curve created by the equation.

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