Question

Determine the zero(s) of the quadratic function y=−5x^2+16x
(1 point)
Responses

(0, 0) and (3.2, 0)
(0, 0) and (3.2, 0)

(-3.2, 0)
(-3.2, 0)

There are no zeros.
There are no zeros.

(0,5) and (0, 16)

Answer 1

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

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

We can factor out \(x\):

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

This gives us two equations to solve:

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

Now, let's solve the second equation:

\(-5x + 16 = 0\)

Rearranging gives:

\(-5x = -16\)

Dividing both sides by -5:

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

So the zeros of the function are:

\[
x = 0 \quad \text{and} \quad x = 3.2
\]

In coordinate form, the zeros are (0, 0) and (3.2, 0).

Thus, the correct response is:

**(0, 0) and (3.2, 0)**