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 equation \( y = -3x^2 + 12x + 15 \), we need to find the values of \( x \) for which \( y = 0 \).

This leads us to the equation:

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

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 equal to zero gives us the zeros of the equation:

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 coordinates of the zeros are:

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

Among the given options, the correct responses are \( (5, 0) \) and \( (-1, 0) \). Therefore, both of these points indicate where the function intersects the x-axis.