Determine the zero(s) of the quadratic function y=−5x2+16x
.(1 point)
Responses
(−3.2,0)
left parenthesis negative 3.2 comma 0 right parenthesis
There are no zeros.
There are no zeros.
(0,0)(3.2,0)
left parenthesis 0 comma 0 right parenthesis left parenthesis 3.2 comma 0 right parenthesis
(0,5)(0,16)
To determine the zeros of a quadratic function, we need to set y equal to zero and solve for x. In this case, the quadratic function is y = -5x^2 + 16x.
Setting y equal to zero:
0 = -5x^2 + 16x
Next, we can factor out an x from the right side:
0 = x(-5x + 16)
Now, we have two equations to solve for x:
1) x = 0
2) -5x + 16 = 0
For equation 1, when x = 0, y is also 0. So we have the zero (0,0).
For equation 2, we can solve for x by isolating it:
-5x + 16 = 0
-5x = -16
x = 16/5
This gives us the zero (3.2, 0).
Therefore, the zeros of the quadratic function y = -5x^2 + 16x are (0,0) and (3.2,0). Answer choice (0,0) (3.2,0) is the correct response.
To determine the zero(s) of a quadratic function, you need to find the values of x for which y equals zero. In this case, the quadratic function is y = -5x^2 + 16x.
To find the zeros, you can set y equal to zero and solve for x:
-5x^2 + 16x = 0
To solve this quadratic equation, you can factor out an x:
x(-5x + 16) = 0
Now, you have two factors:
x = 0 or -5x + 16 = 0
For the first factor, x = 0, which means that one of the zeros is x = 0.
For the second factor, -5x + 16 = 0, you can solve for x by isolating the variable:
-5x = -16
Dividing both sides by -5:
x = 3.2
Therefore, the zeros of the quadratic function y = -5x^2 + 16x are x = 0 and x = 3.2.
In coordinate form, the zeros can be written as:
(0, 0) and (3.2, 0).
To determine the zeros of a quadratic function, we need to set the function equal to zero and solve for x.
In this case, the quadratic function is y = -5x^2 + 16x.
Setting y = 0, we have:
0 = -5x^2 + 16x
Next, we can try factoring the quadratic expression. However, in this case, it cannot be factored easily.
Alternatively, we can use the quadratic formula to find the zeros of the function. The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
For our quadratic function, a = -5, b = 16, and c = 0.
Plugging these values into the quadratic formula, we get:
x = (-16 ± √(16^2 - 4(-5)(0))) / (2(-5))
Simplifying further, we have:
x = (-16 ± √(256)) / (-10)
This simplifies to:
x = (-16 ± 16) / (-10)
This yields two possible solutions:
x = (0) / (-10) = 0
x = (-32) / (-10) = 3.2
Therefore, the zeros of the quadratic function y = -5x^2 + 16x are: (0, 0) and (3.2, 0).