For the given quadratic equation convert into vertex form, find the vertex, and find the value for x = 6. Show your work.
y = -2x2 + 2x +2
-(1/2)y = x^2 - x - 1
(-1/2)y + 1 = x^2 - x
(-1/2)y + 1 = (x - 1/2)^2 - 1/4
(-1/2)y = (x-1/2)^2 - 5/4
y = -2(x-1/2)^2 + 5/2
would this be correct?
you are correct
thank you!
Yes, your conversion of the quadratic equation into vertex form is correct. The vertex form of a quadratic equation is given by y = a(x - h)^2 + k, where (h, k) represents the coordinates of the vertex. In this case, the equation is y = -2(x - 1/2)^2 + 5/2. Here, the vertex is located at (1/2, 5/2).
To find the value of y when x = 6, substitute x = 6 into the equation y = -2(x - 1/2)^2 + 5/2:
y = -2(6 - 1/2)^2 + 5/2
y = -2(11/2)^2 + 5/2
y = -2(121/4) + 5/2
y = -242/4 + 5/2
y = -121/2 + 10/2
y = -111/2
Therefore, when x = 6, the value of y is -111/2.