1 Ch 5 Pt 3 (5-7 & 5-8) Portfolio Page -- Algebra 2 Lesson 5-7: Solving Quadratic Equations --By Completing the Square Examples: Steps to Solving Equations by Completing the Square 1) Get x terms on one side in descending order and the constant term on the other 2) Divide (if necessary) to get a coefficient of 1 on the squared term 3) Add the number needed to complete the square to both sides 4) Write one side as a binomial square, simplify the other 5) Take square root of each side 6) Solve for x. Find vertex by completing the square: Steps: 1) Separate x terms (descending order) and constant term; add and subtract the number needed to complete the square. 2) Use the first three terms to write a binomial square; combine other two terms 3) Write the ordered pair for the vertex.

2 𝑥= −𝑏± 𝑏 2 −4𝑎𝑐 2𝑎 Lesson 5-8: Quadratic Formula--Solve quadratic equations using Quadratic Formula --Use discriminant to determine # and type of solutions Examples: Quadratic formula *equation must FIRST be in standard form ax2 + bx + c = 0 𝑥= −𝑏± 𝑏 2 −4𝑎𝑐 2𝑎 The Discriminant: Finding # and Type of Solutions: The radicand b2 – 4ac is called the discriminant  If b2 – 4ac > 0, the equation has _____ _________ solution(s). If b2 – 4ac = 0, the equation has _____ _________ solution(s). If b2 – 4ac < 0, the equation has _____ __________ solution(s).