the function has zeros -1 and 3 and maximum value of 8?

Hello

let us assume that it is a parabola.

You can write the equation of a parabola as

y = ax^2 + bx + c

or as its vertex form

y = a(x-xV)^2 + yV

where xV and yV are the coordinates of the vertex.

Then what you know are the zeros and the vertex. The x-value of the vertex must be in the middle between the two zeros = +1, and the y value is 8.

So you can write the equation of the parabola in the vertex form:

y = a(x-1)^2 + 8

to find a use the coordinates of a zero:

0 = a(3 -1)^2 + 8

0 = a(2)^2 + 8

0=4a + 8

a = - 2

so the equation is

y = -2(x-1)^2 + 8 or

y = -2x^2 + 4x +6

http://www.wolframalpha.com/input/?i=-2x%5E2%2B4x%...

Regards