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

(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

There are no zeros.

1 answer

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

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

Now, we can either use the quadratic formula or factor the equation. First, let’s simplify it by dividing every term by -3:

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

Next, we can factor this quadratic equation:

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

Setting each factor equal to zero gives us:

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

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

The zeros of the equation are \( x = 5 \) and \( x = -1 \). So, we can express the zeros as points:

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

Therefore, the correct response is:

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

So the answer is:

(−1, 0)(5, 0)