Explanation
Correct answer: B.
Choice B is correct. The given quadratic expression is in standard form, and each answer choice is in vertex form. Completing the square converts the expression from standard form to vertex form. The first step is to rewrite the expression as follows: . The first three terms of the revised expression can be rewritten as a perfect square as follows: . Combining the constant terms gives .
Desmos solution:
Note: The regression uses the listed x-values to fit k=-5, matching (x+3)^2-5.
Enter in Desmos:
Reviewed and rewritten by CookSAT
Why the other choices are wrong
Choice A
Choice A is incorrect. Squaring the binomial and simplifying the expression in choice A gives . Combining like terms gives , not .
Choice C
Choice C is incorrect. Squaring the binomial and simplifying the expression in choice C gives . Combining like terms gives , not .
Choice D
Choice D is incorrect. Squaring the binomial and simplifying the expression in choice D gives . Combining like terms gives , not .