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

Question

Responses

(−3.2,0)
left parenthesis negative 3.2 comma 0 right parenthesis

(0,5)(0,16)
left parenthesis 0 comma 5 right parenthesis left parenthesis 0 comma 16 right parenthesis

(0,0)(3.2,0)
left parenthesis 0 comma 0 right parenthesis left parenthesis 3.2 comma 0 right parenthesis

There are no zeros.

Answer 1

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

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

We can factor this equation:

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

Setting each factor equal to zero gives us the solutions:

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

Solving for \( x \) in the second equation:

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

Thus, the zeros of the function are:

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

This means the points are \( (0, 0) \) and \( (3.2, 0) \).

Therefore, the correct response is:

\[ (0,0)(3.2,0) \]

So the answer is \( \left(0, 0\right) \) and \( \left(3.2, 0\right) \).