Math Is Fun Forum

redXI

Member

Registered: 2008-02-24

Posts: 3

Quartic functions(Simple but confusing)

Hi everyone. So I was trying to study for the upcoming test and I  stumbled on these two questions on my book that puzzled me.

1. The function f(x)=x^4+ax^3-4x^2+bx+6 has x-intercepts (2,0) & (-3,0). Find the values of a & b.

2. The functions y= (a-2b)x^4-3x-2 & y=x^4-x^3+(a+5b)x^2-5x+7 both have an x-intercept of 1. Find the value of a & b.

I've tried solving it but I messed up in the process. I also have this parabola question from my previous test that I can't seem to answer perfectly:

The parabola has a turning point at (z,-8); it intersects the y-axis at y=10 and one of the x intercepts is x=5. Find the value of z and equation of parabola.

So, I really hope people are eager to help me solving my seemingly simple questions. I am a responsible student and I learn fast. Thanks!

Last edited by redXI (2008-02-24 23:37:55)

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Quartic functions(Simple but confusing)

For each of 1 and 2, substitute the values of x and f(x) or y directly and solve the simultaneous equations in a and b.

For the parabola, there are two possible equations, depending on whether the turning point is to the left or to the right of the given x-intercept.

Since the parabola passes through (0,10), (5,0) and (z,−8),

Hence

Also, the turning point is at x=z:

From [1]:

So:

So

And from [1]

The two possible equations of the parabola are

And the two possible values of z = −b⁄2a:

Last edited by JaneFairfax (2008-02-25 01:21:10)

redXI

Member

Registered: 2008-02-24

Posts: 3

Re: Quartic functions(Simple but confusing)

Awesome. I can do it now. Thanks.