Answer:Here are the steps to find the vertex of the quadratic equation y = 2x^2 + 8x - 2:
The vertex form of a quadratic equation is:
y = a(x- h)^2 + k
Where (h,k) are the coordinates of the vertex.
In this equation, a = 2, b = 8, c = -2. To find the vertex (h,k):
h = -b / (2a)
= -8 / (2(2))
= -2
k = y when x = h
= y when x = -2
Substitute x = -2 into the original equation:
y = 2(-2)^2 + 8(-2) - 2
= 8 - 16 - 2
= -10
Therefore, the vertex of this parabola is:
(h,k) = (-2, -10)
We can verify this graphically:
Plugging y = 2x2 + 8x - 2 into a graphing calculator and adding the point (-2, -10), we can see that the point sits at the bottom of the parabola, verifying it is the vertex.
So in summary, the vertex of the quadratic equation y = 2x^2 + 8x - 2 is:
(-2, -10)
Hope this explanation of the steps and solution is helpful! Let me know if you have any other questions.
Explanation: