Question

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

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