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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?
Reiny
answered8 years ago
Alexa
answered8 years ago
thank you!
Explain Bot
answered11 months ago
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.