Find the coordinates of the vertex of the graph y= -x^2+2
Y = -X^2 + 2.
h = Xv = -b/2a = 0/-2 = 0.
k = Yv = 0^2 + 2 = 2.
V(h,k) = V(0,2).
To determine the coordinates of the vertex of the graph of a quadratic equation in the form y = ax^2 + bx + c, where a, b, and c are constants, you can use the formula for the x-coordinate of the vertex:
x = -b / (2a)
In the given equation, y = -x^2 + 2, we can see that a = -1, b = 0, and c = 2.
Using the formula, we can calculate the x-coordinate of the vertex:
x = -0 / (2 * (-1))
x = 0
To find the y-coordinate of the vertex, substitute the value of x into the original equation:
y = -(0)^2 + 2
y = 2
Therefore, the coordinates of the vertex of the graph y = -x^2 + 2 are (0, 2).