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.

Answer 1

Complete the square to identify the vertex of y=x2−16x+14
.(1 point)
Responses

(8,−50)
left parenthesis 8 comma negative 50 right parenthesis

(8,78)
left parenthesis 8 comma 78 right parenthesis

(8,30)
left parenthesis 8 comma 30 right parenthesis

(8,14)

Answer 2

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

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

To make it easier to solve, let's divide the entire equation by -3:

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

Next, we can factor the quadratic:

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

Now, we set each factor equal to zero:

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

Thus, the zeros of the function are \( x = 5 \) and \( x = -1 \).

Therefore, the points (or zeros) are:

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

The correct response is:

**(−1,0)(5,0)**