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**4.8 Quadratic Formula and Discriminant**

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**Quadratic Formula Formula: x = -b ± √(b2 – 4ac) 2a**

This formula can be used to solve any quadratic equation. Equations must be written in standard form. Identify: a = b = c = When solving the formula use order of operations.

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Examples: Solve the equations below: (Ex1) x2 + 3x = 2

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**Equation with One Solution**

Solve the equation below: (Ex2) 25x2 – 18x = 12x – 9

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**Equation with Imaginary Solution**

Solve the equation below: (Ex3) -x2 + 4x = 5

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**Discriminant Formula: b2 – 4ac**

Discriminant informs you how many and what type of solutions there are to a quadratic equation. Types of Solutions: 1) # > real solutions 2) # = real solution 3) # < imaginary solutions

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**Examples: How many solutions are there to the equation below?**

x2 – 8x + 17 = 0

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**Determine if the equation has a real solution or an imaginary solution.**

7x2 – 2x = 5

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