Question

Determine the zero(s) of the quadratic function y=−5x2+16x .(1 point)
Responses

(−3.2,0)
left parenthesis negative 3.2 comma 0 right parenthesis

There are no zeros.
There are no zeros.

(0,0)(3.2,0)
left parenthesis 0 comma 0 right parenthesis left parenthesis 3.2 comma 0 right parenthesis

(0,5)(0,16)

Answer 1

To find the zeros of the quadratic function \( y = -5x^2 + 16x \), we set \( y = 0 \) and solve for \( x \):

\[
0 = -5x^2 + 16x
\]

Factoring out \( x \):

\[
0 = x(-5x + 16)
\]

This gives us two factors:

1. \( x = 0 \)
2. \( -5x + 16 = 0 \)

Now, solving for \( x \) in the second equation:

\[
-5x + 16 = 0 \implies 5x = 16 \implies x = \frac{16}{5} = 3.2
\]

So, the zeros are:

1. \( x = 0 \)
2. \( x = 3.2 \)

Thus, the zeros of the function are \( (0, 0) \) and \( (3.2, 0) \).

The correct response is:

(0,0)(3.2,0)