x^3+ 2x^2 - 3x + 4 = ??

Question

mathmale · Answer

Some thought required here.  First, you could assume that this graph represents a polynomial.  You may (or may not) be able to determine the exact polynomial.

Four dots appear on the graph, each representing a particular point (with x- and y-value).  Note how you have two roots / solutions.

I'd suggest you list all of the points, estimating the one for which x is approx. 1.4 (which represents a root of the polynomial).  If you make that into a dot, you'll then have FIVE dots representing 5 points on the curve.

you could use the model

y= ax^5 + bx^4 + cx^3 + dx^2 + ex + f

which has 6 unknown coefficients:  { a, b, c, d, e, f }.

Please read this through and then tell me which part of my comments make sense to you and which do not.

mathmale · Answer

I'm suggesting we ignore the x-intercept that is unmarked.
That leaves us with FOUR dots, right?
Four dots => four points on graph => Fourth order polynomial with 5 coefficients.

mathmale · Answer

Let the polynomial be 

$$f(x)=ax^4+bx^3+cx^2 +dx +e$$

mathmale · Answer

You'll see that the first point is (0,3).  Take the function I just gave you; let f(0) = 3.  This results in$$f(0)=3=a*0^4 +b*0^3+c*0^2+d*0 +e$$

mathmale · Answer

what is the value of e?

mathmale · Answer

And what was that other something that y ou were supposed to find?

mathmale · Answer

Hint:  3=0+0+0+0+e, so e=?

mathmale · Answer

sorry...OpenStudy was down for a few minutes.

If you have four black dots on the given graph, that means we can find the values of only four (not five) coefficients, { a, b, c, d }.

Thus, discard the fourth-order model, above, and adopt the third-order model

$$f(x) = ax^3 +bx^2+cx+d$$If you now focus on the first point (the black dot at (0,3), and let f(0)=3, then d = 3.

Then $$f(x)=ax^3+bx^2+cx+3.$$
Now, look at the other three dots.  Substitute the x and y-values into the above equation for each point.  Each time you do this, you will have found the value of one more coefficient.  You will end up knowing the coeff. { a, b, c, d }.

Write out the polynomial using these known (numerical) coeff. instead of the lettters { a, b, c, d } to represent the coeff.

Then you're done!

Unfortunately, I have to get off the Internet now.  But if you need further help, simply respond here, and I will see your message next time I'm on OpenStudy.

mathmale · Answer

I've returned.  Need any further help / suggestions?