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

Question

(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)