Completing the Square by Factoring Out -1

At about the 0:34 mark, the teacher says our goal is to get it into...standard form; he should have said get it into vertex form.

At about the 4:42 mark, the teacher writes ±sqrt(5)=x+2; he should have written ±sqrt(5)=x-2. Because of this, he also gets the wrong zeros; he should get x=2±sqrt(5).

This lesson teaches completing the square by factoring out -1. After isolating the x-terms and making it into a binomial square, students can add and subtract the constant value inside the trinomial, which can be multiplied by the -1 factor. This will provide a perfect square trinomial that can be written in binomial square format. Through solving for the zeros, students can determine the value of x, and avoid common mistakes such as not factoring out the negative one or forgetting to divide it first before taking the square root.

Completing the square by factoring out a negative one

• How do I complete the square when there is a negative sign in front of the x^2 term?
• How do I get a quadratic equation that is in standard form into vertex form?
• How do I find the zeros of a quadratic function?
• How do I complete the square on the function f(x)=-x^2+4x+1?
• How do I get -x^2+4x+1 into vertex form?
• What are the zeros of the function f(x)=-x^2+4x+1?