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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)

1 answer

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)