Question

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

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

We can factor out \( x \):

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

This gives us two factors:

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

Now, let's solve \( -5x + 16 = 0 \):

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

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

In coordinate form, these points are \( (0, 0) \) and \( (3.2, 0) \).

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

The correct response is \( (3.2, 0) \).