Worksheet Key 9 11/14/2018 8:58 PM 4.8 - Quadratic Formula.

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Presentation transcript:

Worksheet Key 9 11/14/2018 8:58 PM 4.8 - Quadratic Formula

Worksheet Key (x)2 + 1 11/14/2018 8:58 PM 4.8 - Quadratic Formula

11/14/2018 8:58 PM 4.8 - Quadratic Formula

Quiz 11/14/2018 8:58 PM 4.8 - Quadratic Formula

Quadratic Formula Section 4.8 11/14/2018 8:58 PM

Discriminant Standard form equation, ax2 + bx + c = 0 Discriminant is from standard form, the expression, b2–4ac indicates how many real number solutions the equation has To Determine Solutions: POSITIVE – 2 Real Solutions ZERO – 1 Solution, Double Root NEGATIVE – 2 Imaginary Solutions 11/14/2018 8:58 PM 4.8 - Quadratic Formula

Discriminant: 4, 2 Real Solutions Example 1 Determine the amount of solutions for this equation and the discriminant of x2 – 4x + 3 = 0 Identify A, B, C first A: 1, B: –4, C: 3 Plug into equation, b2 – 4ac (–4)2 – 4(1)(3) 16 – 12 4 Discriminant: 4, 2 Real Solutions 11/14/2018 8:58 PM 4.8 - Quadratic Formula

Discriminant: 0, 1 Double Root Example 2 Determine the amount of solutions for this equation and the discriminant of x2 = 8x – 16 Discriminant: 0, 1 Double Root 11/14/2018 8:58 PM 4.8 - Quadratic Formula

Discriminant: –23, 2 Imaginary Roots Example 3 Determine the amount of solutions for this equation and the discriminant of –2x2 – 5x – 6 = 0 Discriminant: –23, 2 Imaginary Roots 11/14/2018 8:58 PM 4.8 - Quadratic Formula

Discriminant: –223, 2 Imaginary Roots Your Turn Determine the amount of solutions for this equation and the discriminant of 2x2 + x + 28 = 0 Discriminant: –223, 2 Imaginary Roots 11/14/2018 8:58 PM 4.8 - Quadratic Formula

Quadratic Formula Quadratic Formula from Completing the Square 11/14/2018 8:58 PM 4.8 - Quadratic Formula

Quadratic Formula Quadratic Formula from Completing the Square 11/14/2018 8:58 PM 4.8 - Quadratic Formula

Quadratic Formula Quadratic Formula from Completing the Square 11/14/2018 8:58 PM 4.8 - Quadratic Formula

Quadratic Formula Quadratic Formula is another way of finding x Steps: Make sure the equation equals to zero Identify A, B, C Plug into equation Check your work 11/14/2018 8:58 PM 4.8 - Quadratic Formula

Quadratic Formula 11/14/2018 8:58 PM 4.8 - Quadratic Formula

Quadratic Formula X equals negative B, plus or minus square root, b squared minus 4 A C, all over 2 A 11/14/2018 8:58 PM 4.8 - Quadratic Formula

Example 4 Solve x2 – 4x + 3 = 0 using Quadratic Formula A: 1, B: –4, C: 3 11/14/2018 8:58 PM 4.8 - Quadratic Formula

Example 4 Solve x2 – 4x + 3 = 0 using Quadratic Formula A: 1, B: –4, C: 3 11/14/2018 8:58 PM 4.8 - Quadratic Formula

Example 5 Solve 2x2 – 5x = –3 using Quadratic Formula 11/14/2018 8:58 PM 4.8 - Quadratic Formula

Example 6 Solve x2 + 12x + 9 = 0 using Quadratic Formula A: 1, B: 12, C: 9 11/14/2018 8:58 PM 4.8 - Quadratic Formula

Example 6 Solve x2 + 12x + 9 = 0 using Quadratic Formula A: 1, B: 12, C: 9 11/14/2018 8:58 PM 4.8 - Quadratic Formula

Example 7 Solve 9x2 – 11 = 6x using Quadratic Formula 11/14/2018 8:58 PM 4.8 - Quadratic Formula

Your Turn Solve 2x2 – 10 = 4x using Quadratic Formula 11/14/2018 8:58 PM 4.8 - Quadratic Formula

Assignment Worksheet 11/14/2018 8:58 PM 4.8 - Quadratic Formula