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

Question

Responses

(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.

(−1,0)(5,0)

Answer 1

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

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

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

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

Now, we need to factor the quadratic equation:

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

Setting each factor equal to zero gives us:

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

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

Therefore, the correct answer is \( (-1, 0) \) and \( (5, 0) \).