1. Introduction and Review Skills
Conic Sections
Introduction and Review Skills

2. Slope and Midpoint Formula
Ex: Find the midpoint of a line passing through the points (5,3) & (-3, 5)
Ex: Find the midpoint of a line passing through the points
(-4, -3) & (-2, 5)

3. Distance Formula Distance Formula: d= 𝑥2 −𝑥1 2+ 𝑦2−𝑦1 2
Example #1: Find the distance between the points
(5,3) & (-3, 5)
Example #2: Find the distance between the points
(-4, -3) & (-2, 5)

4. Completing the Square
This is another method to solve quadratic equations: 𝑎 𝑥 2 +𝑏𝑥+𝑐=0
Other methods are:
Quadratic Formula
Factoring

5. Completing the Square Steps:
Example: Solve by completing the square:
𝑥 2 +10𝑥+21=0
Step 1: Make sure the equation is set equal to 0
Step 2: Always make sure the 1st coefficient is a one, if not, divide the entire equation by the coefficient
Step 3: Move the constant to the other side
𝑥 2 +10𝑥=−21
Create “boxes” in the equation
𝑥 2 +10𝑥 =−21+

6. Completing the Square Steps:
Step 4: Divide middle term by 2, circle it, square it
𝑥 2 +10𝑥 =−21+
10 2 =5 2 =25
Step 5: Put that value in the boxes
𝑥 2 +10𝑥+ 25 =−21+25
Step 6: Create the perfect square trinomial:
𝑥+5 2 =4

7. Completing the Square Steps:
Step 7: Solve for x, you will have two solutions
𝑥+5 2 =4
𝑥 = 4
𝑥+5 =±2
𝑥=−3, 𝑥=−7

8. Solve by completing the square:
Example: 𝑚2 + 10𝑚 + 22 =1
Answers: 𝑚=−7, 𝑚=−3

9. Solve by completing the square:
Example: 2𝑛2 + 12𝑛 + 10 = 0
Answers: n=−3, 𝑛=−2

10. Solve by completing the square:
Example: 5𝑛2+20𝑛 −380 =5
Answers: n=−11, 𝑛=7