To find the zeros of the quadratic equation \( y = -3x^2 + 12x + 15 \), we can set the equation to zero and solve for \( x \):
\[ -3x^2 + 12x + 15 = 0 \]
To simplify the equation, we can divide everything by -3:
\[ x^2 - 4x - 5 = 0 \]
Next, we can factor the quadratic:
\[ (x - 5)(x + 1) = 0 \]
Setting each factor to zero gives us the possible solutions:
\[ x - 5 = 0 \quad \Rightarrow \quad x = 5 \] \[ x + 1 = 0 \quad \Rightarrow \quad x = -1 \]
Thus, the zeros of the quadratic equation are \( x = 5 \) and \( x = -1 \).
In coordinate notation, the zeros are:
\[ (-1, 0) \quad \text{and} \quad (5, 0) \]
Therefore, the correct response would be:
(−1, 0) and (5, 0).
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