By completing the square, the second order polynomial in vertex form f(x) = (x + 3)² - 6 is equivalent to the polynomial in standard form f(x) = x² + 6 · x + 3. (Correct choice: B)
How to find the vertex form of the second order polynomial by algebraic means
In this question we must change the form of the second order polynomial from standard form into vertex form. A common method consists in completing the square, that is, to transform part of the polynomial into a perfect square trinomial. Now we proceed to find the vertex form of the expression:
1) x² + 6 · x + 3 Given
2) x² + 6 · x + 9 - 6 Modulative property/Existence of additive inverse/Definition of addition
3) (x + 3)² - 6 Associative property/Perfect square trinomial/Result
By completing the square, the second order polynomial in vertex form f(x) = (x + 3)² - 6 is equivalent to the polynomial in standard form f(x) = x² + 6 · x + 3. (Correct choice: B)
To learn more on second order polynomials in vertex form: https://brainly.com/question/20333425
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