Determine the zero(s) of the quadratic function y=−5x^2+16x . (1 point) Responses (0,0) (3.2,0) (0,0) (3.2,0) (0,5) (0,16) (0,5) (0,16) There are no zeros. There are no zeros. (-3.2,0)
The zeros of a quadratic function occur when the y-value is equal to zero. To find the zeros, we need to set y = 0 and solve for x.
0 = −5x^2 + 16x
To solve this equation, we can factor:
0 = x(−5x + 16)
Setting each factor equal to zero, we get:
x = 0 or −5x + 16 = 0
For the first equation, x = 0, we have one zero: (0,0).
For the second equation, −5x + 16 = 0, we solve for x:
−5x = −16
x = 16/5 or 3.2
So, the other zero is (3.2, 0).
Therefore, the zeros of the quadratic function y = −5x^2 + 16x are (0, 0) and (3.2, 0).