Homework 67: p.529: EOO, All Homework 68: p.536: EOO, Odd

Transcription

1 9.4/9.5: Solving Quadratic Equations Homework 67: p.529: 2-49 EOO, All Homework 68: p.536: EOO, 77-8 Odd Objectives Solve Quadratic Equations by Graphing Solve Quadratic Equations by the Quadratic Formula Entry Task: Simplify each radical expression

2 Concept: Solutions to an Equation Solution to a Quadratic Equation: Any values for x where: ax 2 + bx + c = 0 is true

3 Example : Simple Quadratics and Their Graphs Solve and Graph 2 x2 = x2 = 8 2 x 2 = 6 x = ± = = 8 2 (6) = 8

4 Example : Simple Quadratics and Their Graphs 2 x2 = x2 8 = 0 x x2 + 8 y (x, y) , , 6 (0, 8) (2, 6) (4,0)

5 Example : Simple Quadratics and Their Graphs Solution = x-intercept Solution = x-intercept Solution: x = 4 Root: x = 4 Solution: x = 4 Root: x = 4 Vertex/y-intercept

6 Student Led Example : Parabolas and Their Graphs We ll get to this in a second but first, why we don t rely on hand drawn graphs

7 Concept: Minimums and Maximums If a parabola opens upward, the vertex is a minimum If a parabola opens downward, the vertex is a maximum

8 Activity: Solving Quadratics with a Calculator Given the function 2 x2 + 2x 6: A. Find the x-intercepts B. Find the y-intercept C. Find the Vertex D. Find the Axis of Symmetry

9 Activity: Solving Quadratics with a Calculator Given the function 2 x2 + 2x 6: A. Find the x-intercepts Step : Input the function into Y= Step 2: Press 2 nd and Calc, then choose option 2, Zero

10 Activity: Solving Quadratics with a Calculator Given the function 2 x2 + 2x 6: A. Find the x-intercepts Step 3: Set the Left and Right Bounds for each of the x-intercepts. Then, guess close to the intercept

11 Activity: Solving Quadratics with a Calculator Given the function 2 x2 + 2x 6: B. Find the y-intercept IT S THIS. There is nothing more you need to do. It s THIS NUMBER!

12 Activity: Solving Quadratics with a Calculator Given the function 2 x2 + 2x 6: C. Find the Vertex Step 5: Determine if the function opens up or opens down. Step 6: Press 2 nd and Calc, then choose option either Maximum or Minimum

13 Activity: Solving Quadratics with a Calculator Given the function 2 x2 + 2x 6: C. Find the Vertex Step 7: Use Left and Right bound and Guess the minimum. It s safe to round Vertex = ( 2, 8) Axis of symmetry

14 Example 2: Parabolas as Solutions [Discussion Only] You and your buddies developed a sling shot large enough to hurl a softball sized snowball across your neighborhood. An angle of 35 degrees to 65 degrees is found to be your sweet spot for carnage. After tracking the path of a few snowballs, you get two equations: y 35 = x x + 6 y 65 = x x + 6 Which angle provides the greatest distance? Which provides the greatest height?

15 Example 2: Parabolas as Solutions If a 35 angle reaches 56 feet and a 65 angle reaches 73 feet, what angle would you use to hit that annoying kid that is 60 feet from your launcher?

16 The Quadratic Formula x = b + b 2 b 2 4ac 4 c 2 a

17 Example 3: The Quadratic Formula Solve x 2 + 9x + 4 b ± b 2 4ac 2a a =, b = 9, c = 4 9 ± 9 2 4()(4) 2()

18 Example 3: The Quadratic Formula Solve x 2 + 9x ± 9 2 4()(4) 2() 9 ± ± 25 2

19 Example 3A: The Quadratic Formula Solve x 2 + 9x ± ± = = 4 = 2 = 7 2 2

20 Example 3A: The Quadratic Formula Solve x 2 + 9x + 4 possible solutions: x = { 7, 2} x 2 + 9x + 4 x 2 + 9x + 4 ( 7) 2 +9( 7) + 4 ( 2) 2 +9( 2)

21 Example 3B: The Quadratic Formula Solve 2x 2 3x = 8 Write in Standard Form: 2x 2 3x 8 = 0 b ± b 2 4ac 2a ( 3) ± ( 3) 2 4(2)( 8) 2(2)

22 Example 3B: The Quadratic Formula Solve 2x 2 3x = 8 ( 3) ± ( 3) 2 4(2)( 8) 2(2) 3 ± ± 73 4

23 Student Led Example 3: The Quadratic Formula Solve each quadratic function using the quadratic formula A x 2 + 3x = 2 C 2 + x 2 = x x = 2 x = 2, B 3x 2 + 7x 20 D x 2 2x 2 x = 5 3, 4 x = ± 2 3

24 End of Lesson None. I think SLE 3 was enough work to count as an exit task.