Warm Up ~ Unit 2 Day 1 Solve by factoring: 3

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Presentation transcript:

Warm Up ~ Unit 2 Day 1 Solve by factoring: 3 𝑥 2 −48=0 12 𝑥 2 =𝑥 Simplify the radicals: −45 𝑏. 128 Simplify (3−2𝑖)(5+𝑖)

Quadratic Formula and the Discriminant

Types of Roots of a Quadratic Function One-Real Solution Two-Real Solutions No Real Solutions

Quadratic equations can be solved using different methods... FACTORING GRAPHING QUADRATIC FORMULA

Quadratic Formula: https://www.youtube.com/watch?v=HRcj9slciqM https://www.youtube.com/watch?v=2lbABbfU6Zc https://www.youtube.com/watch?v=-gwz6d9NYz0 https://www.youtube.com/watch?v=b1q1pPI79TY

Quadratic Formula Make sure to use the standard form of a Quadratic Equation: Ax2 + Bx + C = 0 First: Get Quadratic in Standard Form Second: Identify a, b, and c Third: Substitute into the formula and find the answers. Fourth: Simplify!!!!

Use the Quadratic Formula to solve each equation: Your equation must be set = 0 to use the formula!!!!  3x2 – 5x – 2 =0 Steps: Standard Form = 0 Identify a, b, and c Substitute values into formula Simplify *Remember to leave answers as reduced fractions whenever needed.

1) 3x2 – x = 4 2) 9x2 = -6x – 1 3) x2 + 3x – 5 = 0 4) -2x2 = 4x + 3

You Try! Use the Quadratic Formula to solve :

Discriminant: Is the number under the radical in the quadratic formula: b2 - 4ac The discriminant tells us how many real solutions there are to a problem. …Remember we said there are always solutions, they just aren’t always real!

If the discriminant > 0 then there are 2 real solutions If the discriminant = 0 then there is 1 real solution If the discriminant < 0 then there are 0 real solutions and 2 non-real solutions

Using the Discriminant: Find the discriminant of the quadratic equation and use it to find the number and type of solutions.

Homework!! HW 2-3