Use any method to locate the zeros of y = −3x^2 + 12x + 15.

A) (1, 0) (-5, 0)
B) (0, 15)
C) There are no zeros
D) (-1, 0) (5, 0)

1 answer

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 \( x \):

\[ -3x^2 + 12x + 15 = 0 \]

We can simplify this equation by dividing all terms by -3:

\[ x^2 - 4x - 5 = 0 \]

Next, we can factor the quadratic equation:

\[ (x - 5)(x + 1) = 0 \]

Setting each factor to zero gives us:

  1. \( x - 5 = 0 \) → \( x = 5 \)
  2. \( x + 1 = 0 \) → \( x = -1 \)

The zeros of the function correspond to the points where the function intersects the x-axis. Thus, we have the zeros at:

\[ (5, 0) \quad \text{and} \quad (-1, 0) \]

Therefore, the correct answer is:

D) (-1, 0) (5, 0)