Findthevertexoftheparabolay = x2 + 4x + 6.Simplify both coordinates and write them as proper fractions, improper fractions, or integers.
Question
Find the vertex of the parabola
Simplify both coordinates and write them as proper fractions, improper fractions, or integers.
Solution
To find the vertex of the parabola given by the equation y = x^2 + 4x + 6, we can use the formula for the x-coordinate of the vertex of a parabola, which is -b/2a, where a and b are the coefficients of x^2 and x, respectively, in the equation of the parabola.
In this case, a = 1 (the coefficient of x^2) and b = 4 (the coefficient of x), so the x-coordinate of the vertex is -b/2a = -4/(2*1) = -2.
To find the y-coordinate of the vertex, we substitute the x-coordinate of the vertex into the equation of the parabola. So, y = (-2)^2 + 4*(-2) + 6 = 4 - 8 + 6 = 2.
Therefore, the vertex of the parabola y = x^2 + 4x + 6 is (-2, 2).
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