The vertex form of the equation y = -x^2 + 4x - 1 is y = -(x - 2)^2 + 3
<h3>How to determine the vertex form of the quadratic equation?</h3>
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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(-7, -1) i confirmed and the distance between both -7, -1 and 1,5 to center is 5.
So -1 is the answer!
The x-axis is the real axis, and the y-axis is the positive imaginary (i) axis.
So the number w is approximately -1+3i.
Two ways to solve the problem.
1.
-i w = -i (-1+3i) = -i (-1)+ (-i)(3i) = +i +3, so the answer is the point A.
2.
You can consider multiplying by i is a counter-clockwise rotation of 90 degrees, and -i is a -90 degrees (i.e. clockwise). So we can rotate w by -90 degrees to get point A.