Question

Use any method to locate the zeros of y=−3x2+12x+15.(1 point) Responses There are no zeros. There are no zeros. (0,15) left parenthesis 0 comma 15 right parenthesis (−1,0)(5,0) left parenthesis negative 1 comma 0 right parenthesis left parenthesis 5 comma 0 right parenthesis (1,0)(−5,0)

Answer 1

To locate the zeros of the quadratic function \( y = -3x^2 + 12x + 15 \), we can set \( y \) 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 the quadratic:

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

Setting each factor to zero gives us the solutions:

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

Thus, the zeros of the function are \( x = 5 \) and \( x = -1 \).

The corresponding points where the function crosses the x-axis are:

- For \( x = 5 \), the point is \( (5,0) \).
- For \( x = -1 \), the point is \( (-1,0) \).

So, the correct response is:

**(−1,0) and (5,0)**.