The vertex form of the equation y = -x^2 + 4x - 1 is y = -(x - 2)^2 + 3
The quadratic equation is given as:
y = -x^2 + 4x - 1
Differentiate the above quadratic equation.
This is done with respect to x by first derivative
So, we have:
y' = -2x + 4
Set the derivative to 0
-2x + 4 = 0
Subtract 4 from both sides of the equation
-2x + 4 - 4 = 0 - 4
Evaluate the difference in the above equation
-2x = -4
Divide both sides of the above equation by -2
x = 2
Rewrite as
h = 2
Substitute 2 for x in the equation y = -x^2 + 4x - 1
y = -2^2 + 4 *2 - 1
Evaluate the equation
y = 3
Rewrite as:
k = 3
A quadratic equation in vertex form is represented as:
y = a(x - h)^2 + k
So, we have:
y = a(x - 2)^2 + 3
In the equation y = -x^2 + 4x - 1, a = -1
So, we have:
y = -(x - 2)^2 + 3
Hence, the vertex form of the equation y = -x^2 + 4x - 1 is y = -(x - 2)^2 + 3
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