Determine the zero(s) of the quadratic function y=−5x^2+16x
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To find the zeros of the quadratic function y = -5x^2 + 16x, we set y = 0 and solve for x.
0 = -5x^2 + 16x
Rearranging the equation:
5x^2 - 16x = 0
Factoring out x:
x(5x - 16) = 0
Setting each factor equal to zero:
x = 0
5x - 16 = 0
Solving for x:
5x = 16
x = 16/5
Therefore, the zeros of the quadratic function y = -5x^2 + 16x are x = 0 and x = 16/5.
To determine the zero(s) of a quadratic function, we need to find the value(s) of x when the function y is equal to zero. In other words, we are looking for the x-values where the graph of the quadratic function intersects the x-axis.
In the given quadratic function y = -5x^2 + 16x, we set y equal to zero:
0 = -5x^2 + 16x
To solve this equation, we can use factoring, completing the square, or the quadratic formula. Let's use factoring in this example.
First, let's rearrange the equation:
-5x^2 + 16x = 0
Next, let's factor out common terms:
x(-5x + 16) = 0
Now we have two possibilities for the equation to be true:
1) x = 0
2) -5x + 16 = 0
For the first possibility, if x = 0, then the value of y will also be 0. Therefore, (0, 0) is one of the zero points.
For the second possibility, let's solve the equation -5x + 16 = 0 for x:
-5x + 16 = 0
-5x = -16
x = -16/-5
x = 16/5
So, the second zero point is (16/5, 0).
Therefore, the quadratic function y = -5x^2 + 16x has two zero(s) at x = 0 and x = 16/5.
To determine the zero(s) 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 for x, we can use factoring, completing the square or the quadratic formula. Factoring isn't possible in this case, so let's use the quadratic formula:
The quadratic formula states that for a quadratic equation of the form ax^2 + bx + c = 0, the solutions for x can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, 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))
x = (-16 ± √(256)) / (-10)
x = (-16 ± 16) / (-10)
The two possible solutions are:
x = (-16 + 16) / (-10) = 0 / (-10) = 0
x = (-16 - 16) / (-10) = (-32) / (-10) = 3.2
Therefore, the zero(s) of the quadratic function y = -5x^2 + 16x are x = 0 and x = 3.2.