1. Bellwork Use the distributive property to find each product. 1. (x+2)(x -5) 2. (-3x+2)(2x-6) Identify whether each function is quadratic. 3. f(x) = 4x³ - 8x² 2x 4. f(x)= -2x + 8 State whether the parabola opens up or down and whether the y-coordinate of the vertex is the minimum value or maximum value of the function. Then, find the coordinates of its vertex. 5. f(x) =(3-x)(2+x) 6. f(x) = 4 – x + x²

2. Lesson 5.2 Introduction to Solving Quadratic Equations

3. Notes on Lesson 5.2 Solving Quadratic Equations Solving Equations of the Form x² = a If a≥ 0, then x = or x = - EXAMPLE #1 4x² + 13 = 253 Exact Answer: x = ± Approximate Answer: x≈7.75

4. Notes on Lesson 5.2 Solving Quadratic Equations Solving Equations of the Form x² = a If a≥ 0, then x = or x = - EXAMPLE #2 9(x-2)² = 121

5. Notes on Lesson 5.2 Solving Quadratic Equations Solving Equations of the Form x² = a If a≥ 0, then x = or x = - EXAMPLE #3 7(x+1)² = 161 Exact Answer: Approximate Answer:

6. #1) x²-12 = 4 Answer: x = ±4 #2) 5x²- 4 = 96 Exact Answer: x = ± Approximation: x≈ 4.47

7. #3) 6x² + 15 = 23

8. #4) 12= 4(x-2)² - 8

9. What if a there is a negative under the square root? It isn’t that Complex…We will use our imaginations!!!! Example

10. What if a there is a negative under the square root? It isn’t that Complex…We will use our imaginations!!!! Example

11. Using the Pythagorean Theorem If ABC is a right triangle with the right angle at C, then a²+b²=c² Hypotenuse (c) Side (a) Side (b) Parts of a right triangle.

12. Practice: Find the unknown length in each right triangle. Give answers to the nearest tenth. x 7cm 9cm Solution: a² +b² = c² 7² + 9² = c² 49 + 81 = c² 130 = c² c≈ 11.4 cm

13. Practice: Find the unknown length in each right triangle. Give answers to the nearest tenth. 13cm 6cm x Solution: a² +b² = c² 6² + b² = 13² 36 + b² = 169 c² = 133 c≈ 11.5 cm

14. Worksheet 5.2A