Introduction and Review Skills Conic Sections Introduction and Review Skills

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)

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)

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

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+

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: 2 𝑥+5 2 =4

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

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

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

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