Ch 9: Quadratic Equations B) Square Roots Objective: To solve quadratic equations using square roots.

Quadratic Expression An expression in which 2 is the largest exponent. ax 2 + bx + c Quadratic Equation An equation in which 2 is the largest exponent. ax 2 + bx + c = 0 Square root of a quadratic The square root of a variable squared (x 2 ) equals the absolute value of the square root. Definitions = |x| = ± x

1)Isolate x 2 (get x 2 on one side and the number on the other side) 2) Take the square root of BOTH sides (keep the equation balanced) 3) Solve for the absolute value of x (this creates 2 equations) Look to see if the number is on the diagonal of the multiplication table. (a) If so, it is a perfect square and you have your answer. (Don’t forget the ± symbol) (b)If not, simplify the radicand and solve for both equations Note: There should be two answers! Rules

Multiplication Table x Perfect Squares

Two Solutions x 2 = 12 √x 2 = √ 2  2  3 |x| = 2√3 x = ±2√3 Two Solutions x 2 = -9 √x 2 = √-9 No Real solution √x 2 = √ On the DiagonalNot on the DiagonalNegative on the inside Example 1Example 2Example 3

y = y 2 = 5 Example 4Example 5Example 6 2m 2 − 3 = m 2 = 8 2 m 2 = 4 3r = 8 −7 3r 2 = 1 3

y = 2 x = 3 ± y 2 = -2 No Real Solution Example 7Example 8Example 9

x 2 = 18x 2 – 4 = 12 √x 2 = √18 |x| = √2  3  3 x = ± 3√2 + 4 x 2 = 16 √x 2 = √16 |x| = ± 4 1)2)3) Classwork

4) 5) 6) 2

7) 8) No Real Solution