Question

Use any method to locate the zeros of y=−3x2+12x+15
.(1 point)
Responses

(1,0)(−5,0)
left parenthesis 1 comma 0 right parenthesis left parenthesis negative 5 comma 0 right parenthesis

There are no zeros.
There are no zeros.

(0,15)
left parenthesis 0 comma 15 right parenthesis

(−1,0)(5,0)

Answer 1

To locate the zeros of the quadratic equation \( y = -3x^2 + 12x + 15 \), we need to set \( y \) to zero and solve for \( x \):

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

We can simplify the equation by dividing every term by -3:

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

Next, we can factor the quadratic:

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

Setting each factor equal to zero gives us the potential zeros:

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

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

In coordinate form, these zeros can be expressed as points on the graph:

- \( (5, 0) \)
- \( (-1, 0) \)

Therefore, the correct response is:

\[
(-1, 0)(5, 0)
\]