Question

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

There are no zeros.
There are no zeros.

(0,0)(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

(0,5)(0,16)

Answer 1

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

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

We can factor out \( x \) from the equation:

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

Setting each factor equal to zero, we get:

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

For the second equation:

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

Thus, the zeros of the function are:

1. \( x = 0 \)
2. \( x = 3.2 \)

The points where the function intersects the x-axis are \( (0, 0) \) and \( (3.2, 0) \).

Therefore, the correct response is:

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