Warm-Up 2.10 Solve the following. 8x2 + 18x + 9 = 0

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Presentation transcript:

Warm-Up 2.10 Solve the following. 8x2 + 18x + 9 = 0 Answers: x = -1.5 or x = -0.75

. Teacher (Magnani) Algebra 3 Lesson 2.10 Objective: SSBAT solve a quadratic equations through graphing the equation and finding the x- intercepts. Standards: M11.D.4.1.1

Solving A Quadratic Equation Find all the x-values that make the equation true. Also referred to as: Finding the zeros/roots/x-intercepts X-Intercept  Point where the graph crosses the x-axis

Solving Quadratic Equations through Graphing Make the equation equal to 0 (if it is not already) 2. Graph the equation 3. Find the x-intercepts 4. The solutions are the x-intercepts

Finding the x-intercepts (zeros) in the Calculator Enter the equation into y= (top left button) Hit Graph (top right button) Go to 2nd Trace Choose #2 – Zeros Scroll cursor over until it is sitting on the far left x-intercept Hit the LEFT Arrow key twice Hit enter Move the cursor back to the x-intercept it was just on Hit the RIGHT Arrow key twice Hit Enter Hit Enter when it says Guess The x-value that appears is one of the solutions Continue on Next Slide

Finding the x-intercepts (zeros) in the Calculator Hit 2nd Trace Number 2 15. Scroll cursor over until it is sitting on the far right x-intercept 14. Hit the LEFT Arrow key twice 15. Hit enter 16. Move the cursor back to the x-intercept it was just on 17. Hit the Right Arrow key twice 18. Hit Enter 19. Hit Enter when it says Guess 20. The x-value that appears is the other solution

Examples: Solve each equation through graphing. x2 – x – 12 = 0 Answers: x = -3 and x = 4

Examples: Solve each equation through graphing. 3x2 – 2x – 8 = 0 . Teacher (Magnani) Examples: Solve each equation through graphing. 3x2 – 2x – 8 = 0 . Answers: x = -1.33 and x = 2

Examples: Solve each equation through graphing. 3. 8x2 – 14x = 15 8x2 – 14x – 15 = 0 Answers: x = 2.5 and x = -0.75

Examples: Solve each equation through graphing. 4. -5x2 + 14 = -7x -5x2 + 7x + 14 = 0 Answers: x = -1.11 and x = 2.51

Examples: Solve each equation through graphing. 5. 3x2 + 4x + 6 = 0 Answers: No Real Solution

Complete Worksheet 2.10