Question

Determine the zero(s) of the quadratic function y=−5x^2+16x .(1 point) Responses There are no zeros. There are no zeros. (0,5)(0,16) left parenthesis 0 comma 5 right parenthesis left parenthesis 0 comma 16 right parenthesis (0,0)(3.2,0) left parenthesis 0 comma 0 right parenthesis left parenthesis 3.2 comma 0 right parenthesis (−3.2,0) left parenthesis negative 3.2 comma 0 right parenthesis

Answer 1

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

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

Next, we can factor out the common term \( x \):

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

This equation will equal zero if either \( x = 0 \) or \( -5x + 16 = 0 \).

1. From \( x = 0 \), we have one zero at \( (0, 0) \).
2. Now, let's solve \( -5x + 16 = 0 \):

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

This gives us another zero at \( (3.2, 0) \).

Thus, the zeros of the function \( y = -5x^2 + 16x \) are \( (0, 0) \) and \( (3.2, 0) \).

The correct response from the given options is:

**(3.2, 0)**.