1. Welcome to the MM218 Unit 7 Seminar To resize your pods: Place your mouse here. Left mouse click and hold. Drag to the right to enlarge the pod. To maximize chat, minimize roster by clicking here

2. MM218 Unit 7 Seminar Agenda Square Root Property Completing the Square Quadratic Formula Discriminant

3. The Square Root Property If x 2 =a, then x = ±√[a] for all real numbers a Example: Solve x 2 =25 Answer, x = ±√[25] = ±5 (which means, x = 5 or x = -5)

4. Completing the Square One way to solve a quadratic equation Steps: 1) Put into form ax 2 +bx+c=0 2) Make sure a=1, if not-divide by “a” to make it so 3) Square half the coefficient of the linear term and add to both sides 4) Factor the left into a perfect square 5) Use the Square Root Property to solve

5. Completing the Square Example: Solve by completing the square x 2 +6x+8=0 1) Put into form ax 2 +bx=-cx 2 +6x=-8 2) Make sure a=1, if not-dividea=1 already by “a” to make it so 3) Square half the coefficient of the x 2 +6x +(6/2) 2 =-8 +(6/2) 2 linear term and add to both sidesx 2 +6x +(3) 2 = 1 4) Factor the left into a perfect square (x+3) 2 = 1 5) Use Square Root Property to solve (x+3) = ±√[1] = ±1 x+3 = 1 or x+3 = -1 x = -2 or x = -4 x = -4, -2

6. Completing the Square Example: Solve by completing the square 3x 2 +4x-2=0 1) Put into form ax 2 +bx=-c 2) Make sure a=1, if not-divide by “a” to make it so 3) Square half the coefficient of the linear term and add to both sides 4) Factor the left into a perfect square 5) Use Square Root Property to solve

7. Quadratic Formula For all equations ax 2 +bx+c=0,

8. Quadratic Equation Example: Solve using the quadratic equation 2x 2 +5x=-1

9. Discriminant In the Quadratic Formula, the expression b 2 -4ac is called the discriminant If the discriminant D is: The Quadratic Equation has: Positive 2 Real Solutions Zero 1 Real Solution Negative2 Complex Solutions

10. Discriminant Example: What type of solutions does the equation have? a)x 2 +6x+8=0 b) 5x 2 +10x+9=0 c) x 2 -8x=-16