Determine the zero(s) of the quadratic function y=−5x2+16x .(1 point) Responses (0,5)(0,16) left parenthesis 0 comma 5 right parenthesis left parenthesis 0 comma 16 right parenthesis (−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)

Answer 1

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

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

We can factor out \( x \):

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

This gives us two factors:

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

Solving the second factor:

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

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

In coordinate form, the zeros are:

1. \( (0, 0) \)
2. \( (3.2, 0) \)

Among the given options, the correct response is:

(3.2, 0).