To find the zeros of the quadratic function \( y = -3x^2 + 12x + 15 \), we can set the equation equal to zero and solve for \( x \):
\[ -3x^2 + 12x + 15 = 0 \]
We can simplify this equation by dividing all terms by -3:
\[ x^2 - 4x - 5 = 0 \]
Now, we can factor the quadratic:
\[ (x - 5)(x + 1) = 0 \]
Setting each factor equal to zero gives us:
\[ x - 5 = 0 \quad \Rightarrow \quad x = 5 \] \[ x + 1 = 0 \quad \Rightarrow \quad x = -1 \]
Thus, the zeros of the function are \( x = 5 \) and \( x = -1 \). Therefore, the corresponding points where \( y = 0 \) are \( (5, 0) \) and \( (-1, 0) \).
The correct answer is:
(5,0) and (-1,0).