Determine the zero(s) of the quadratic function y=−5x2+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.
To determine the zero(s) of the quadratic function, we need to find the value(s) of x where y = 0.
Given the function y = -5x^2 + 16x, we set it equal to 0 and solve for x:
-5x^2 + 16x = 0
Now, we can factor out x:
x(-5x + 16) = 0
This equation will be true when either x = 0 or -5x + 16 = 0.
1. x = 0
If we substitute x = 0 into the equation, we have -5(0)^2 + 16(0) = 0, which is true.
2. -5x + 16 = 0
Solving this equation, we have:
-5x = -16
Divide both sides by -5:
x = -16/-5
x = 3.2
Therefore, the zeros of the quadratic function y = -5x^2 + 16x are (0, 0) and (3.2, 0). So, the correct answer is: (0, 0) and (3.2, 0).