The equation y2+3=2(2x+y) represents a parabola with the vertex at
Question
The equation y2+3=2(2x+y) represents a parabola with the vertex at
Solution
To find the vertex of the parabola represented by the equation y^2 + 3 = 2(2x + y), we first need to rewrite the equation in vertex form. The vertex form of a parabola is y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.
Let's start by simplifying the equation:
y^2 + 3 = 2(2x + y) y^2 + 3 = 4x + 2y y^2 - 2y = 4x - 3 y^2 - 2y + 1 = 4x - 3 + 1 (y - 1)^2 = 4x - 2
Now the equation is in the form (y - k)^2 = 4a(x - h), which is a form of the vertex form for parabolas that open horizontally. The vertex of the parabola is at (h, k), so in this case, the vertex is at (2, 1).
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