Learn on PengiCalifornia Reveal Math, Algebra 1Unit 10: Quadratic Functions

10-5 Solving Quadratic Equations by Completing the Square

In this Grade 9 lesson from California Reveal Math Algebra 1, students learn how to solve quadratic equations by completing the square, including cases where the leading coefficient is not 1. The lesson covers finding the value of c that creates a perfect square trinomial using the pattern x² + bx + (b/2)² = (x + b/2)², then applying the Square Root Property to isolate solutions. Students also use completing the square to convert quadratic functions into vertex form and identify key features such as the axis of symmetry, extrema, and zeros.

Section 1

Complete the Square of x^2 + bx

Property

To complete the square of $x^2 + bx$ :

Step 1. Identify $b$ , the coefficient of $x$ .

Step 2. Find $(\frac{1}{2}b)^2$ , the number to complete the square.

Section 2

Solve Equations by Completing the Square

Property

To solve a quadratic equation of the form $x^2 + bx + c = 0$ by completing the square:

Step 1. Isolate the variable terms on one side and the constant terms on the other.

Step 2. Find $(\frac{1}{2}b)^2$ , the number needed to complete the square. Add it to both sides of the equation.

Lesson overview

Expand to review the lesson summary and core properties.

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Section 1

Complete the Square of x^2 + bx

Property

To complete the square of $x^2 + bx$ :

Step 1. Identify $b$ , the coefficient of $x$ .

Step 2. Find $(\frac{1}{2}b)^2$ , the number to complete the square.

Section 2

Solve Equations by Completing the Square

Property

To solve a quadratic equation of the form $x^2 + bx + c = 0$ by completing the square:

Step 1. Isolate the variable terms on one side and the constant terms on the other.

Step 2. Find $(\frac{1}{2}b)^2$ , the number needed to complete the square. Add it to both sides of the equation.