Question

write the equation of a function whose x-intercepts are -1 and 3, and a range consisting of all numbers less than or equal to 4

Answer 1

So if we had a polynomial with roots (x-intercepts) of -1 and 3, we could write it like this,\[\Large 0=(x+1)(x-3)\]

But this represents a parabola opening `upward`.
We want our x-values to be no larger than 4, hmm. How could we fix that?

Answer 2

flip the direction of the parabola so just make it negative?

Answer 3

Yah that sounds right :)\[\Large 0=-(x+1)(x-3)\]
You might want to multiply that out for a better looking final answer.

Answer 4

The vertex of this parabola is going to be at (1,4).
Oh boy we sure cut it close on that one! :O

Answer 5

yay thanks!!!