1. 9.1c SKM & PP 1 Quadratic Equations

2. 9.1c SKM & PP 2 Square Roots: Know Your Squares! Consider this equation: What number(s) could be squared to give a result of 49? From our knowledge of number facts, we would know that the answer would be: because

3. 9.1c SKM & PP 3 Square Roots: Know how to factor! We could also put the equation in STANDARD FORM and factor to find the solutions.

4. 9.1c SKM & PP 4 Square Roots: Know the Rules! Because this equation has the form: BINOMIAL SQUARE equals NUMBER we can use the SQUARE ROOT PROPERTY! Remember the + because every positive number has two square roots!

5. 9.1c SKM & PP 5 The Square Root Property: x 2 = n and n = 0 has one solution, x = 0. {0}

6. 9.1c SKM & PP 6 The Square Root Property: x 2 = n and n > 0 If n is a positive number, i.e., n > 0, then has two real solutions.

7. 9.1c SKM & PP 7 The Square Root Property: x 2 = n and n < 0 If n is a negative number, i.e., n < 0, then x 2 = n has no Real Solutions. Ø

8. 9.1c SKM & PP 8 The Square Root Property: Summary has one solution, x = 0. If n is a positive number, i.e., n > 0, then has two real solutions. If n is a negative number, i.e., n < 0, then x 2 = n has no Real Solutions.

9. 9.1c SKM & PP 9 General Strategy for Solving a Quadratic Equation by taking the Square Root 1)See that the equation only has the quadratic and the constant terms. 2) Solve the equation for the quadratic variable, the squared variable. 3) Take square roots on both sides of the equation and remember to put + before the radical. 4) Simplify the radical.

10. 9.1c SKM & PP 10 Square Root Property Solve: x 2 = 144

11. 9.1c SKM & PP 11 Square Root Property Solve: 2 x 2 - 100 = 0 25 2

12. 9.1c SKM & PP 12 Square Root Property Solve: 16 x 2 -3=0

13. 9.1c SKM & PP 13 Square Root Property Solve: 7 x 2 -5=0

14. 9.1c SKM & PP 14 Square Root Property Solve: 2 x 2 +18=0

15. 9.1c SKM & PP 15 Square Root Property Solve: 3 x 2 + 5 = 5

16. 9.1c SKM & PP 16 When the Quadratic Equation is missing the linear term, the term with x 1, it is generally a good idea to try the Square Root Property to solve the problem. is the form best suited to using the Square Root Property. This will be important when we study solving quadratic equations by Completing the Square! The Square Root Property ( variable expression ) 2 = #

17. 9.1c SKM & PP 17 That’s All for Now!