Do Now Use the standard form of a quadratic equation to find the a, b and c of each equation. ax2 + bx + c = 0 x2 – 6x + 10 = 0 2x2 + 3x + 4 = 0 x2 –

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Presentation transcript:

Do Now Use the standard form of a quadratic equation to find the a, b and c of each equation. ax2 + bx + c = 0 x2 – 6x + 10 = 0 2x2 + 3x + 4 = 0 x2 – 5x – 7 = 8

3.4 Using the Quadratic Formula Objective: analyze the discriminant to determine the number and type of solutions

You can analyze the discriminant of a quadratic equation to determine the number and type of solutions of the equation.

Examples: Analyzing the Discriminant Find the discriminant of the quadratic equation and describe the type of solution of the equation. a. x2 – 6x + 10 = 0 b. x2 – 6x + 9 = 0 c. x2 – 6x + 8 = 0

Practice: Analyzing the Discriminant Find the discriminant of the quadratic equation and describe the type of solution of the equation. 1. 4x2 + 8x + 4 = 0 2. ½x2 + x – 1 = 0

Practice: Analyzing the Discriminant Find the discriminant of the quadratic equation and describe the type of solution of the equation. 3. 5x2 = 8x – 13 4. 7x2 – 3x = 6

Practice: Analyzing the Discriminant Find the discriminant of the quadratic equation and describe the type of solution of the equation. 5. 4x2 + 6x = – 9 6. –5x2 + 1 = 6 – 10x

The Quadratic Formula x2 + 3x – 5 = 0 Solve using the quadratic formula. x2 + 3x – 5 = 0

Example: Solve using the quadratic formula. x2 – 6x+9 = 0

Practice solving equations with the quadratic formula. x2 + 2x – 3 = 0 2x2 + 4x – 1 = 0 3x2 – 2x – 6 = 0

Homework Section 3.4 Practice A Worksheet

Do Now Determine the number and type of solutions to the equation x2 + 7x = – 11 Two real solutions One real solution Two imaginary solutions One imaginary solution