Find the maxizimum value of y in the eaquation y=1?2x?3(x^2)

To find the maximum value of y in the equation y = 1-2x-3(x^2), we need to find the vertex of the parabola represented by the equation. The vertex will give us the maximum value of y.

Step 1: Rewrite the equation in standard form.
y = -3(x^2) - 2x + 1

Step 2: Identify the coefficients of x^2, x, and the constant term.
In this equation, the coefficient of x^2 is -3, the coefficient of x is -2, and the constant term is 1.

Step 3: Use the formula x = -b/2a to find the x-coordinate of the vertex.
In this case, a = -3 and b = -2. Plugging these values into the formula, we get:
x = -(-2)/(2*(-3))
x = 2/(-6)
x = -1/3

Step 4: Substitute the x-coordinate of the vertex back into the original equation to find the y-coordinate.
y = -3((-1/3)^2) - 2(-1/3) + 1
y = -3(1/9) + 2/3 + 1
y = -1/3 + 2/3 + 1
y = 2/3 + 1
y = 5/3

So, the maximum value of y in the equation y = 1-2x-3(x^2) is 5/3.