To locate the zeros of the quadratic function \( y = -3x^2 + 12x + 15 \), we need to set the equation equal to zero and solve for \( x \):
\[ -3x^2 + 12x + 15 = 0 \]
To simplify the equation, we can divide every term by -3:
\[ x^2 - 4x - 5 = 0 \]
Now, we can solve the quadratic equation using the factoring method, the quadratic formula, or completing the square. Let's first try factoring:
We look for two numbers that multiply to \(-5\) (the constant term) and add to \(-4\) (the coefficient of \(x\)). The numbers that work are \(-5\) and \(1\). Thus, we can factor the equation as follows:
\[ (x - 5)(x + 1) = 0 \]
Setting each factor to zero gives us the potential zeros:
\[ x - 5 = 0 \quad \text{or} \quad x + 1 = 0 \]
Solving these equations results in:
\[ x = 5 \quad \text{and} \quad x = -1 \]
Therefore, the zeros of the function \( y = -3x^2 + 12x + 15 \) are:
\[ x = 5 \quad \text{and} \quad x = -1 \]
We can confirm these solutions by substituting them back into the original equation to verify that they yield zero.
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