Question

Please help, I don't know how to do this.

3. Apply your knowledge of factoring and zero product property to write a quadratic function when given -2 and 2/3 as the zeros. (Show all work for full credit)

Answer 1

3x^2 +4x-4

Explanation:

We know the zeros are -2 and 2/3

Using the zero product property

(x- -2) (x -2/3) = 0

(x+2) (x-2/3) = 0

We want to write the function, so we need to FOIL

first x*x = x^2

outer: -2/3x

inner: 2x

last: -4/3

Add together

x^2 -2/3x +2x -4/3 =0

x^2 -2/3x+6/3x -4/3 =0

x^2 +4/3x - 4/3 =0

We can multiply by any constant and it will still give us the same zeros

I will multiply by 3 to get rid of the fractions

3(x^2 +4/3x - 4/3) =0*3

3x^2 +4x-4 = 0