Test info for chp 10 test – next week 30 problems in total Factoring – 8 Completing the square – 3 Multiplying polynomials – 9 Solve for “x” – 4 Adding/subtracting polynomials – 2 Quadratic equation questions – 4 –# of solutions –What does/do the solution(s) tell you –The type of graph that a quadratic equation makes

5 ways to solve a Quadratic equation SectionMethodComments 9.2Finding square rootsWhen there’s no “b”, ax + c = 0 9.3Graphingused for any Q.E., but is only an approximation 9.4Quadratic formulaUsed for any Q.E., always gives exact answer 10.6factoringEfficient way to solve Q.E. IF it can be factored 10.7Completing the squareUse for any Q.E., best suited when a = 1 & b is an even #

Completing the square Goal of completing the square is to make an equivalent quadratic equation that is a perfect square so that it can be factored. Allows you to solve (find the x-intercepts) a quadratic equation without using the quadratic formula.

Steps for completing the square when the leading coefficient, a = 1 1.Quadratic equation has to first be in standard form 2.Add/Subtract “c” from both sides so that you have ax 2 + bx = c 3.Add (b/2) 2 to both sides – this creates a trinomial squared. 4.Factor the trinomial squared. 5.Find the square roots of both sides of the equation. 6.Solve for “x”

example X 2 – 6x + 7 = 0 Subtract “c” from both sides X 2 – 6x = -7 Add (b/2) 2 to both sides X 2 – 6x + (-6/2) 2 = -7 +(-6/2) 2 X 2 – 6x + 9 = 2 Factor the trinomial squared (x - 3) 2 = 2

Find square roots of both sides of the equation X – 3 = 2 Solve for “x” X =

Let’s try another X x – 11 = 0 X x = 11 X x = X x + 25 = 36 (x + 5) 2 = 36 X + 5 = +/- 6 X = 11, -1

Completing the square when leading coefficient is not equal to 1