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 (0,0)(3.2,0) left parenthesis 0 comma 0 right parenthesis left parenthesis 3.2 comma 0 right parenthesis There are no zeros. There are no zeros. (−3.2,0)
To find the zeros of a quadratic function, we need to set the function equal to zero and solve for x.
Setting y=0, we have:
0 = -5x^2 + 16x
Factoring out an x from the equation, we get:
0 = x(-5x + 16)
Setting each factor equal to zero gives us two possible solutions:
x = 0 and -5x + 16 = 0
For the second equation, solving for x gives us:
-5x + 16 = 0
Subtracting 16 from both sides:
-5x = -16
Dividing both sides by -5:
x = -16/(-5)
x = 3.2
So the zeros of the quadratic function y = -5x^2 + 16x are:
x = 0 and x = 3.2
Therefore, the correct answer is:
(0,0) and (3.2,0)
To determine the zeros of a quadratic function, you need to find the values of x that make the function equal to zero. In this case, the quadratic function is given as y = -5x^2 + 16x.
To find the zeros, you can set the function equal to zero and solve for x. The equation becomes:
-5x^2 + 16x = 0
Now, let's factor out x from the equation:
x(-5x + 16) = 0
Set each factor equal to zero:
x = 0 (Equation 1)
-5x + 16 = 0 (Equation 2)
Now, let's solve Equation 2 for x:
-5x + 16 = 0
-5x = -16
x = -16 / -5
x = 3.2
So, we have two potential zeros: x = 0 and x = 3.2.
Therefore, the correct answer is: (0, 0) and (3.2, 0).
To determine the zeros of the quadratic function y = -5x^2 + 16x, we need to set y equal to zero and solve for x.
0 = -5x^2 + 16x
To solve this quadratic equation, we can either factor or use the quadratic formula. In this case, it's easier to factor out an x:
0 = x(-5x + 16)
Now, we set each factor equal to zero and solve for x:
Case 1: x = 0
When x = 0, the equation is satisfied.
Case 2: -5x + 16 = 0
Adding 5x to both sides:
5x = 16
Dividing both sides by 5:
x = 16/5
So, the zeros of the quadratic function are x = 0 and x = 16/5, which can be written as (0, 0) and (3.2, 0). Therefore, the correct answer is (0, 0) and (3.2, 0).