Determine the zero(s) of the quadratic function y=−5x2+16x

Question

.(1 point)
Responses

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

There are no zeros.

Answer 1

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

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

We can factor out the common term \( x \):

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

This gives us two factors:

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

Now, we solve for \( x \) in the second factor:

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

Thus, the zeros of the function are:

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

So the points at which the function intersects the x-axis (the zeros of the function) are \( (0, 0) \) and \( (3.2, 0) \).

The correct answer is:

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