Polynomial Functions (word problem)

[anonymous12]

Homework Statement

A quartic function has x-intercepts of -5, -1, 2, and 4. The point (3.-8) lies on the curve. Determine an equation of the function.

Homework Equations

The Attempt at a Solution

y = k (x+5)(x+1)(x-2)(x-4)
Expanded form: f(x)=kx^4 + 9x^2 - 38x + 40 <---My expanded form is most likely wrong because expanding a quartic function tends to get clustered and confusing.

Other than this I have absolutely no idea how to solve this question.

 

[gb7nash]

y = k (x+5)(x+1)(x-2)(x-4)

This looks fine.

Expanded form: f(x)=kx^4 + 9x^2 - 38x + 40 <---My expanded form is most likely wrong because expanding a quartic function tends to get clustered and confusing.

Unfortunately, your expansion is wrong. First show your steps, so we can see where the mistake is in your work.

 

[eumyang]

y = k (x+5)(x+1)(x-2)(x-4)
Expanded form...

I wouldn't even expand yet. I would find k first by plugging 3 and -8 for x and y into the factored form. Then I would multiply out the factors, and distribute the k value last.

 

[gb7nash]

Valid point. It's much easier to solve for k in this form.