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# Determine the coefficients of the equation y=ax^3 + bx^2 + cx + d so that it will have critical points at ( 1, 0) and ( -2, 27).

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• mattp222 Mar 25, 2011

What type of calculator do you own?

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I will give you a solution for a ti-83 Plus or ti-84 Plus calculator as they are very similar.

You should hit the [stat] or [stats] button as I forget which it is. Then hit [enter] which will bring you to a stats list editor of some kind. You will want to enter the data for your x-axis in L1 and the data for your y-axis in L2. Once you have completed your lists, hit the [stat] button again and then click [right] or the right arrow in order to move to the section of calc. from number 4 down it will help create a graph of that type of function. You desire a cubic function so it is number 6, so you hit [enter] on number 6 and then you will be at the home screen with CubicReg already written. You just have to complete the statement and it will do it for you. hit the [2nd] [1] and then the comma button, then [2nd] [2] and [enter]. that will do it for you. Also if you want the equation to appear in your y= menu, you can hit [2nd] [stat] and then search for the Y1, but make sure you have a comma between the L2 and the Y1.

Posted on Mar 28, 2011

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## Related Questions:

### How can I solve the aX^3+bX^2+cx+d=0?

There is no easy solution for a cubic equation such as this, unlike a quadratic equation which has a simple solution that we all learnt at secondary school.
Google for cubic or this gives a good explaination

Nov 27, 2014 | Casio FX-82MS Scientific Calculator

It seems to me that you are trying to solve the quadratic equation
aX^2+bX+c=10 with a=-3, b=3, c=15 or -3X^2+3X+15=0.
Since the all the coefficients are multiples of 3, one can simplify the equation by dividing every thing by 3, leaving -X^2+X+5=0. But to avoid confusing you I will consider the original equation -3X^2+3X+15=0..
You must first find out if the equation has any real solutions. To do that you calculate the discriminant (you do not have to remember the name if you choose to).
Discriminant is usually represented by the Greek letter DELTA (a triangle)
DELTA =b^2-4*a*c =(3)^2-4*(-3)*(15)=189
If the discriminant is positive (your case) the equation has two real solutions which are given by
Solution1 =X_1=(-3-SQRT(189))/(-2*3)=(1+SQRT(21))/2
Solution2 =X_2=(-3+SQRT(189))/(-2*3)=(1-SQRT(21))/2 or about -1.791287847
Here SQRT stands for square root.

Aug 17, 2014 | Computers & Internet

### How can i solve quadratic equation (aX^2+bX+c=0) with my BA II plus texas instrument calculator?

The BAIIPlus doesn't have anything specifically for solving quadratic equations. You can simply plug the coefficients a, b, and c into the quadratic formula.

Oct 03, 2013 | Texas Instruments Office Equipment &...

### What are the equations and its kinds?

Definition

A mathematical statement used to evaluate a value. An equation can use any combination of mathematical operations, including addition, subtraction, division, or multiplication. An equation can be already established due to the properties of numbers (2 + 2 = 4), or can be filled solely with variables which can be replaced with numerical values to get a resulting value. For example, the equation to calculate return on sales is: Net income Ã· Sales revenue = Return on Sales. When the values for net income and sales revenue are plugged into the equation, you are able to calculate the value of return on sales.

There are many types of mathematical equations.

1. Linear Equations y= mx + b (standard form of linear equation)
2. Quadratic Equations y= ax^2+bx+c
3. Exponential Equations y= ab^x
4. Cubic Equations y=ax^3+ bx^2+cx+d
5. Quartic Equations y= ax^4+ bx^3+ cx^2+ dx+ e
6. Equation of a circle (x-h)^2+(y-k)^2= r^2
7. Constant equation y= 9 (basically y has to equal a number for it to be a constant equation).
8. Proportional equations y=kx; y= k/x, etc.

Jun 14, 2011 | Computers & Internet

### How to find roots of a polynomial using fx 115 ms

It depends on the degree of the polynomial.
If polynomial is od degree 2 or 3 you can use the EQN mode (the equation MODE) by pressing [MODE][5:EQN] to enter Equation mode then press [3] for quadratic polynomial or [4] for a cubic one.
You will then be prompted for the various coefficients. The canonical form of these polynomials is aX^2 plus bX plus c= 0, and aX^3 plus bX^2 plus cX plus d=0.

If polynomial is of degree higher than 3, or for a general non-linear equation you must use the Solve( feature. See example #017 on page 6 of the appendix to the manual.

Nov 28, 2010 | Casio FX-115ES Scientific Calculator

### Can I factor a polynomial with a Casio fx-9750GII calculator

The short story is that this calculator does have a computer algebra system or CAS and thus cannot factor polynomials with arbitrary (unknown) coefficients or known coefficients.
However if the coefficients are given you can ,if you are willing to travel that way, factor approximately a polynomial P(x).
Basically, the idea is that any polynomial P(X) of degree n can be written in the factored form (X-x_1)(X-x_2)...(X-x_n), where x_1, x_2, x_3,...x_n are the roots (real or complex) of the equation P(X)=0.

The procedure ( for a 3rd degree polynomial) is as follows: (the fixYa site parser will remove the plus signs, so I am writing the whole word plus instead of the mathematical sign
If you want to factor a cubic polynomial P3(X) = aX^3 plus bX^2 plus cX plus d , you write the corresponding cubic equation as aX^3 plus bX^2 plus cX plus d =0 , then you divide all terms of the equation by a to obtain

X^3 plus (b/a)X^2 plus (c/a)X plus (d/a)=0.

You use the calculator to solve (approximately) this equation.
Suppose you find the 3 roots X1,X2,and X3. Then the polynomial X^3 plus (b/a)X^2 plus (c/a)X plus (d/a) can be cast in the factored form (X-X1)(X-X2)(X-X3) and the original polynomial P3(X) can be written as

P3(X) = a*(X-X1)(X-X2)(X-X3)

You can handle the quadratic polynomial the same way.
P2(X) =a*(X-X1)(X-X2) where X1, X2 are the two real roots.

To find the various roots you must use the solve( application.

Nov 11, 2010 | Casio FX-9750GPlus Calculator

### How to you factor trinomials

The short story is that this calculator does have a computer algebra system or CAS and thus cannot factor polynomials with arbitrary (unknown) coefficients or known coefficients.
However if the coefficients are given you can ,if you are willing to travel that way, factor approximately a polynomial P(x).
Basically, the idea is that any polynomial P(X) of degree n can be written in the factored form (X-x_1)(X-x_2)...(X-x_n), where x_1, x_2, x_3,...x_n are the roots (real or complex) of the equation P(X)=0.

The procedure ( for a 3rd degree polynomial) is as follows:
If you want to factor a cubic polynomial P3(X) = aX^3 bX^2 cX d , you write the corresponding cubic equation as aX^3 bX^2 cX d =0 , then you divide all terms of the equation by a to obtain

X^3 (b/a)X^2 (c/a)X (d/a)=0.

You use the calculator to solve (approximately) this equation.
Suppose you find the 3 roots X1,X2,and X3. Then the polynomial X^3 (b/a)X^2 (c/a)X (d/a) can be cast in the factored form (X-X1)(X-X2)(X-X3) and the original polynomial P3(X) can be written as

P3(X) = a*(X-X1)(X-X2)(X-X3)

You can handle the quadratic polynomial the same way.
P2(X) =a*(X-X1)(X-X2) where X1, X2 are the two real roots.

Sep 11, 2010 | Casio FX-9750GPlus Calculator

### Do i have only one type of exponencial regression o my 9850gb plus?

Hello,
Th CFX-9850GB Plus is programmed to perform 10 types of regressions, namely
LinearReg: Linear y=ax+b
Med-Med also linear y=ax+b
Cubic: y=ax^3+bx^2+cx+d
Quartic: y=ax^4+bx^3+cx^2+dx+e
LogReg, logarithmic: y=a+b*ln(x)
ExpReg, exponential y=a*e^(bx)
PowerReg, power: y= ax^b
SinReg, sinusoidal: y=a*sin(bx+c) +d
LogisticReg, logistic; y= c/(1+a*e^(-bx))

There may be more regression models appropriate for more advanced (specialized) statistics but the ones in the list are all the CFX-9850GB plus offers. However, since the calculator knows a programming language, you may want to implement a particular model.

Hope that helps.

Oct 24, 2009 | Casio CFX 9850GB Plus Calculator

### How do I use the solve function

Hello,
First of all, you have to set the mode to EQUATION by pressing [MODE][5:Equation]. When you do that, you are offered 4 choices of equation types to solve.

PART 1 a_n*X+b_n*Y=C_n.

In this type, you have only 2 unknows, X, Y, the others are coefficients. When this mode is selected, you are given access to a what looks like a matrix.
The top row, inaccessible to you, displays headings a, b, c.
The first column, also inaccessible to you numbers the lines as (1 and 2)
First line
Enter the coefficient of X in the first equation, a_1, and press [=] Cursor moves to the dark rectangle under the b heading.
Enter the coefficient of Y, (b_1) in the first equation and press [=] Cursor moves to the dark rectangle under heading c.
Enter the constant term in the first equation, C_1, and press [=]

At this stage you have finished entering the coefficients and constant term of the first linear equation of your system, namely
a_1*X+b_1*Y= C_1

After you enter C_1 and press [ENTER] the cursor moves to the

Second Line

On this line, just as in the previous one, you enter a_2, b_2 and c_2 Once you finish entering all coefficients and constant terms you press [ENTER].

Calculator does its thing and returns with a solution and displays at the top left of the screen
X=
and on the bottom right the value for X ( a fraction or a decimal number)
Press [=] again and the screen displays the value of the second unknown Y.
If you press [=] a third time the claculator takes you back to the entry screen to modifiy coefficients and constant terms.

Exemple a_1=6 b_1=3 c_1=7 a_2=5 b_2=8.3 c_2=1
X= 19/12 To convert it to decimal press [S<->D] to get 1.58333 Y=-5/6 To convert it to decimal press [S<->D] to get -0.8333333

PART B a_n*X+b_n*Y+c_n*Z =D_n This is a linear system in 3 unknowns X, Y, X.
It requires
a_1, b_1, c_1, and d_1
a_2, b_2, c_2, and d_2
a_3, b_3, c_3 and d_3.
Procedure to enter the coefficients and constant terms is the same as above, but due to the limited screen, you have to use right arrow to access the places where you enter d_1, d_2. d_3.

When finished you have to press [=] 1 time to get X, a second time to get Y, and a third time to get Z.

PART C aX^2 + bX +c=0 (quadratic equation)
You enter a, b, and c in the template.

When finished press[ENTER] once to get X1, and a second time to get X2.

PART D aX^3 +bX^2+cX+d =0 (cubic equation)

Same procedure as Part C, except that you have to enter a, b, c, and d in template and press [=] 1 time to get X1, a second time to get X2, and a third time to get X3.

Hope it helps.

PS to the power that be of this site, if you are listening: We ought to have prompts to confirm the post before validating it. We ought to be able to correct typos, errors; to amend what we entered.

Oct 11, 2009 | Casio FX-115ES Scientific Calculator

### How to factor a polynomial equation on casio fx-300es?

Hello,
The Casio FX-300ES does not handle symbolic algebra. So it cannot factor a general polynomial expression. The methods can be found in any book on Algebra.
However if you are interested in approximate factorization of quadratic and cubic polynomials, you can use the calculator to do that. It can solve aX^3 +bX^2+cX+d =0 and the quadratic equations.

If you want to factor a cubic polynomial P3(X) = aX^3+bX^2+cX+d , you write the corresponding cubic equation as aX^3+bX^2+cX=d =0 , then you divide all terms of the equation by a to obtain

X^3+(b/a)X^2+(c/a)X+(d/a)=0.

You use the calculator to solve (approximately) this equation.
Suppose you find the 3 roots X1,X2,and X3. Then the polynomial X^3+(b/a)X^2+(c/a)X+(d/a) can be cast in the factored form (X-X1)(X-X2)(X-X3) and the original polynomial P3(X) can be written as

P3(X) = a*(X-X1)(X-X2)(X-X3)

You can handle the quadratic polynomial the same way.

P2(X) =a*(X-X1)(X-X2) where X1, X2 are the two real roots

Hope it helps.

Sep 27, 2009 | Casio fx-300ES Calculator

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