Question

Determine the zero(s) of the quadratic function y=−5x^2+16x .(1 point) Responses (0,5)(0,16) left parenthesis 0 comma 5 right parenthesis left parenthesis 0 comma 16 right parenthesis (−3.2,0) left parenthesis negative 3.2 comma 0 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 a quadratic function, we set y equal to zero and solve for x:

0 = -5x^2 + 16x

Now we can factor out an x:

0 = x(-5x + 16)

This equation is equal to zero if either x = 0 or -5x + 16 = 0.

1. x = 0
Substituting x = 0 back into the original equation, we find that y = 0. Therefore, the point (0, 0) is a zero of the function.

2. -5x + 16 = 0
Adding 5x to both sides and then dividing by 5, we get:
5x = 16
x = 16/5 = 3.2

Substituting x = 3.2 back into the original equation, we find that y = -5(3.2)^2 + 16(3.2) = 0. Therefore, the point (3.2, 0) is also a zero of the function.

So, the zeros of the quadratic function y = -5x^2 + 16x are (0, 0) and (3.2, 0).

The correct answer is (0, 0)(3.2, 0).