functions. please help

[homeschool girl]

Let [MATH]f(x)[/MATH] be a quadratic polynomial such that [MATH]f(-4) = -22,[/MATH] [MATH]f(-1)=2[/MATH], and [MATH]f(2)=-1.[/MATH] Let [MATH]g(x) = f(x)^{16}. [/MATH]Find the sum of the coefficients of the terms in [MATH]g(x)[/MATH] that have even degree. (For example, the sum of the coefficients of the terms in [MATH]-7x^3 + 4x^2 + 10x - 5[/MATH] that have even degree is [MATH](4) + (-5) = -1.[/MATH]) don't know where to start

 

[Prof]

Looking at the first sentence, you have f(x) = ax^2 + bx + c. Then you have three points you can plug into for x and f(x). If you substitute each point in, you will get 3 different equations with a, b, and c unknown, and you can solve them. If you are using technology, you can use quadratic regression on a graphing calculator.

 

[Steven G]

f(x) is a quadratic, so f(x) = ax^2 + bx + c. There are three unknowns, a, b and c. You have been given three points for f(x). Using those three points will give you 3 equations in 3 unknowns. You can then solve for a, b and c and therefore know what f(x) is. See what you can do with this.

 

[homeschool girl]

[MATH]a=-\frac32, b=\frac12, c=4[/MATH]?

 

[homeschool girl]

so now i need to figure out [MATH](-\frac32x^{2}+\frac12x+4)^{16}[/MATH]?

 

[pka]

so now i need to figure out [MATH](-\frac32x^{2}+\frac12x+4)^{16}[/MATH]?

SEE THE EXPANSION HERE

 

[Steven G]

so now i need to figure out [MATH](-\frac32x^{2}+\frac12x+4)^{16}[/MATH]?

Yes. But pka already did this for you.

 

[pka]

Yes. But pka already did this for you.

I will say for the record that I suspect that the \(16\) is a misprint for that gives seventeen even power terms each of which has a huge coefficient. I can see not point whatsoever to such a question except busywork.