Algebra 2: Resources and Extra Practice - 2.05 Completing the Square

Algebra 2: Resources and Extra Practice

2.05 Completing the Square

Essential Question:

How can completing the square aid in solving quadratic functions?
What indicators predict that a quadratic function will have a complex solution?

Lesson205.mp4

Lesson 2.05 Video - If the video does not load correctly, Click Here to watch.

Khan Academy Resources

Worked example: Completing the square (intro)Sal completes x²-44x into a perfect square.

Finding the vertex of a parabola in standard formSal rewrites the equation y=-5x^2-20x+15 in vertex form (by completing the square) in order to identify the vertex of the corresponding parabola.

Worked example: completing the square (leading coefficient ≠ 1)Sal solves the equation 4x^2+40x-300=0 by completing the square.

Completing the squareSome quadratic expressions can be factored as perfect squares. For example, x²+6x+9=(x+3)². However, even if an expression isn't a perfect square, we can turn it into one by adding a constant number. For example, x²+6x+5 isn't a perfect square, but if we add 4 we get (x+3)². This, in essence, is the method of *completing the square*

Worked example: Completing the square (intro)Sal completes x²-44x into a perfect square.

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