The image shows a geometric representation of the function f(x) = x2 – 2x – 6 written in standard form.
1 answer:
The vertex form of the equation of a parabole is (x - h)^2 + k
So you must complete squares to transform x^2 -2x - 6 in its vertex form.
1) convert x^2 - 2x in a square => (x - 1)^2 - 1
2) Add the constant term - 6 => (x - 1)^2 -1 - 6
3) Add similar terms => (x - 1)^2 - 7
You can verify that (x - 1)^2 - 7 is equal to x^2 - 2x - 6:
x^2 - 2x + 1 - 7 = x^2 - 2x - 6. So, do not doubt it, the vertex form is (x - 1)^2 - 7, where the coordinates of the vertex are (1, - 7)
Answer: option A (x - 1)^2 - 7
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