To find the zeros of the quadratic function \( y = -3x^2 + 12x + 15 \), we set \( y \) equal to zero and solve for \( x \):
\[ -3x^2 + 12x + 15 = 0 \]
First, we can simplify this equation by dividing all terms by -3:
\[ x^2 - 4x - 5 = 0 \]
Next, we can factor this quadratic equation:
\[ (x - 5)(x + 1) = 0 \]
Setting each factor equal to zero gives us the solutions:
\[ x - 5 = 0 \quad \Rightarrow \quad x = 5 \] \[ x + 1 = 0 \quad \Rightarrow \quad x = -1 \]
Thus, the zeros of the function are \( x = 5 \) and \( x = -1 \).
To evaluate at these values, we can calculate \( y \) at these points:
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For \( x = 5 \): \[ y = -3(5)^2 + 12(5) + 15 = -75 + 60 + 15 = 0 \]
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For \( x = -1 \): \[ y = -3(-1)^2 + 12(-1) + 15 = -3 - 12 + 15 = 0 \]
Both calculations confirm that the zeros of the function are correct.
Next, let's interpret your options, which seem to imply some coordinate pairs, suggesting you may want to check what happens at \( x = 8 \):
Calculate \( y \) when \( x = 8 \):
\[ y = -3(8)^2 + 12(8) + 15 = -192 + 96 + 15 = -81 \]
Thus, the point \( (8, y) \) corresponds to \( (8, -81) \), which is not one of the options provided.
Since none of the listed points A) (8, 78), B) (8, 30), C) (8, 14), and D) (8, −50) match \( (8, -81) \), please clarify if you meant to ask about the zeros or the value of the function at \( x = 8 \). The zeros of the function \( y = -3x^2 + 12x + 15 \) are indeed \( 5 \) and \( -1 \).