Question

Use any method to locate the zeros of y=−3x2+12x+15
(-1,0)(5,0)

(0,15)
(1,0)(−5,0)

There are no zeros.

Answer 1

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

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

Now, we can factor the quadratic:

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

Setting each factor equal to zero gives us:

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

Thus, the zeros of the function are \( x = 5 \) and \( x = -1 \). Therefore, the corresponding points where \( y = 0 \) are \( (5, 0) \) and \( (-1, 0) \).

The correct answer is:

**(5,0) and (-1,0)**.