Since we are given the zeros for each function, we can write the equation in factored form first, and then we can simplify it into standard form. Remember that if you were to use the zero product property to find the zeros of a quadratic function, you would need to subtract or add the factors to find the zeros.
1. x = -2 and x = -5
(x + 2)(x + 5) = 0
x² + 7x + 10 = 0
2. x = -2 and x = 0
x(x + 2)
x² + 2x = 0
3. x = -2
(x + 2)² = 0
x² + 4x + 4 = 0
Therefore, the answer to question one is x² + 7x + 10 = 0, the answer to question two is x² + 2x = 0, and the answer to question 3 is x² + 4x + 4 = 0.
