Completing the Square
Master Completing the Square in Grade 10 math. Given a quadratic of the form , add the square of half the coefficient of , , to create a perfect sq. Practice with Saxon Algebra 2 examples.
Key Concepts
Given a quadratic of the form $x^2 + bx$, add the square of half the coefficient of $x$, $\left(\frac{b}{2}\right)^2$, to create a perfect square trinomial. $$x^2 + bx + \left(\frac{b}{2}\right)^2 = \left(x + \frac{b}{2}\right)^2$$.
Complete the square for $x^2 + 14x$. Add $\left(\frac{14}{2}\right)^2 = 7^2 = 49$. So, $x^2 + 14x + 49 = (x+7)^2$. Complete the square for $y^2 20y$. Add $\left(\frac{ 20}{2}\right)^2 = ( 10)^2 = 100$. So, $y^2 20y + 100 = (y 10)^2$.
Imagine you have an incomplete puzzle, $x^2 + bx$. To turn it into a neat, perfect square, you need one special piece. This method is the secret to finding it! Just take the coefficient of $x$, which is 'b', chop it in half, and square the result. Adding this magic number completes the puzzle, making your expression perfectly factorable and easy to solve.
Common Questions
What is Completing the Square?
Given a quadratic of the form , add the square of half the coefficient of , , to create a perfect square trinomial. . Always remember to square it!
How do you apply Completing the Square in practice?
Complete the square for . Add . So, . Complete the square for . Add . So, .
Why is Completing the Square important for Grade 10 students?
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