Question

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

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

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

(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.

Answer 1

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

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

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

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

Now, we can factor the quadratic:

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

Setting each factor to zero gives us:

\[
x - 5 = 0 \quad \Rightarrow \quad x = 5
\]
\[
x + 1 = 0 \quad \Rightarrow \quad x = -1
\]

Therefore, the zeros of the function are \( x = 5 \) and \( x = -1 \). This can be expressed as the points:

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

Thus, the correct response is:

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