If f(x) = x2+ 6x + 9, what are the coordinates of the vertex of the graph of f ?
Question
If f(x) = x2+ 6x + 9, what are the coordinates of the vertex of the graph of f ?
Solution
The vertex of a parabola given in the form f(x) = ax^2 + bx + c is at the point (-b/2a , f(-b/2a)).
In the given function f(x) = x^2 + 6x + 9, a = 1 and b = 6.
So, the x-coordinate of the vertex is -b/2a = -6/(2*1) = -3.
Substitute x = -3 into the function to find the y-coordinate:
f(-3) = (-3)^2 + 6*(-3) + 9 = 9 - 18 + 9 = 0.
So, the vertex of the graph of f is at (-3, 0).
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