Question

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

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

There are no zeros.
There are no zeros.

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

(0,5) and (0, 16)

Answer 1

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

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

Next, we can factor the equation:

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

Setting each factor to zero gives:

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

From the second equation, we solve for \( x \):

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

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

The corresponding points where \( y = 0 \) are:

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

Therefore, the correct response is:

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