Warm-Up 5 minutes Solve by completing the square. 1) x2 – 10x + 23 = 0

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Presentation transcript:

Warm-Up 5 minutes Solve by completing the square. 1) x2 – 10x + 23 = 0

Mastery is 80% or better on 5-min check and Indy work. 13.4.1 The Quadratic Formula Objectives: Students will use the quadratic formula to solve quadratic equations. Determine the number of solutions by utilizing the discriminant. Mastery is 80% or better on 5-min check and Indy work.

Concept Dev-The Quadratic Formula If ax2 + bx + c = 0, a = 0, then the quadratic formula gives the solutions of the quadratic equation.

Skill Dev-Example 1 Solve using the quadratic formula. 3x2 – 7x + 2 = 0

Example 1 Solve using the quadratic formula. 3x2 – 7x + 2 = 0

Skill Dev- Example 2 Solve using the quadratic formula. -x2 + x + 1 = 0

Example 2 Solve using the quadratic formula. -x2 + x + 1 = 0

Guided-Practice…Boards Solve using the quadratic formula. Approximate the solutions to the nearest tenth. 1) 2x2 – 4x = 5 2) x2 + 5x = -3

Guided- Practice Use the quadratic formula to find the roots of each polynomial. 1) 6x2 – 6 – 5x 2) 6x2 – 6x - 5

Homework HW PDF Online Quad Formula & Disc

Warm-Up 5 minutes Solve using the quadratic formula. 1) x2 = 8x - 16

To use the quadratic formula to solve quadratic equations Objectives: To use the quadratic formula to solve quadratic equations To use the discriminant to find the number of solutions for a quadratic equation

The Discriminant The expression under the radical, b2 – 4ac, is called the discriminant. We can use the discriminant to determine the number of solutions b2 – 4ac is positive: two real number solutions b2 – 4ac is zero: one real number solution b2 – 4ac is negative: no real number solutions

Skill Dev - Example 1 Determine the number of real solutions, then solve using the quadratic formula. 4x2 – 7x + 2 = 0 b2 – 4ac = 49 – (4)(4)(2) b2 – 4ac = 17 two real solutions

Guided - Practice Determine the number of real solutions, then solve using the quadratic formula. 1) x2 + 5x = -8 2) 4x2 = 8x - 4 3) 4x2 + 4x = 15

Think..Ink..Share Practice Use the discriminant to determine whether the graph of each quadratic function intersects the x-axis in 0,1, or 2 points. 1) y = 3x2 - 5x + 1 2) f(x) = x2 – 3x + 7 3) y = x2 – 12x + 36

What did you learn? Students will use the quadratic formula to solve quadratic equations. Determine the number of solutions by utilizing the discriminant. Mastery is 80% or better on 5-min check and Indy work.