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What you will learn How to solve a quadratic equation using the quadratic formula How to classify the solutions of a quadratic equation based on the discriminant

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Oh Boy! Vocabulary We have learned about a million ways to solve quadratic equations: factoring taking square roots completing the square Clearly, we need another way: the quadratic formula: Objective: 5.6 The Quadratic Formula and the Discriminant

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A, B, and C? When the quadratic equation is in the form ax2 + bx + c = 0 This will give you the values of x that cause the equation to be equal to zero. This also gives you the two points where the graph of the function will cross the x-axis. Objective: 5.6 The Quadratic Formula and the Discriminant

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**What Are Solutions 1 real solution 2 real solutions**

In addition to being the values of x that satisfy the equation (in this case when the function equals zero), the “answers” are the places where the graph of the function crosses the x-axis. A graph can tell you how many solutions a quadratic function has. 1 real solution 2 real solutions No real solutions (imaginary) Objective: 5.6 The Quadratic Formula and the Discriminant

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**An Example – Two Solutions**

Solve 2x2 + x = 5 Check this with your calculator. Objective: 5.6 The Quadratic Formula and the Discriminant

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You Try! Solve: 3x2 + 8x = 35 Objective: 5.6 The Quadratic Formula and the Discriminant

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**An Example – One Solution**

Solve x2 – x = 5x – 9 This equation will only touch the x-axis in one spot. Objective: 5.6 The Quadratic Formula and the Discriminant

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You Try Solve 12x – 5 = 2x2 + 13 Objective: 5.6 The Quadratic Formula and the Discriminant

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**An Example – Two Imaginary Solutions**

Solve –x2 + 2x = 2 If the solution has an “i” in it, the graph never crosses the x-axis. Objective: 5.6 The Quadratic Formula and the Discriminant

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You Try Solve -2x2 = -2x + 3 Objective: 5.6 The Quadratic Formula and the Discriminant

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**The Discrimiwhat? Discriminant**

The discriminant can also tell us what types of solutions there are to a quadratic equation. If the discriminant is > 0, the equation has two real solutions If the discriminant = 0, then the equation has one real solution. If the discriminant is < 0, then the equation has two imaginary solutions. Objective: 5.6 The Quadratic Formula and the Discriminant

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**Example Find the discriminant of the following: x2 – 6x + 10 = 0**

Calculator check! Objective: 5.6 The Quadratic Formula and the Discriminant

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Homework Page 295, even, 28, even, even, all, 78. Objective: 5.6 The Quadratic Formula and the Discriminant

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