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)

When the zeros are - 2 and 2/3

The factors of the equation would be (x + 2) and (x-2/3)

Now you have (x+2) (x-2/3) = 0

Now expand using FOIL:

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

Simplify ad combine like terms:

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

Simplify the numerator:

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

Expand the numerator using FOIL:

3xx + 3x*2-2x-2*2 / 3 = 0

Simplify and combine like terms:

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

Splpit into 3 fractions:

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

Cancel common factors:

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

The quadratic formula is:

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