Quadratic Formula and Discriminants

9-6 Quadratic Formula and the Discriminant

Fill in the Blank

Do Now: Complete the Square to solve the answer. Type your answer in as an ordered pair.

What is the vertex of the following function?

f(x) = x² -8x + 19

The Quadratic Formula

​The Quadratic Formula gives solutions of the quadratic equation in the form of ax²+bx+c=0 for real values of a, b, and c. The quadratic formula is a useful method to find the solution of ANY quadratic equation.

Multiple Choice

What is the maximum number of solutions a quadratic formula can give?

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Use the Quadratic Formula

​https://www.youtube.com/watch?v=r4Fdt8W0kYU

Multiple Choice

What is the "b" value of the following quadratic equation?

x² - 8 = 2x

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• -2

• -8

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Open Ended

Find the solutions to the equation using the quadratic formula. Round to the nearest tenth if needed.

$$x^2-8=2x$$  

The Discriminant

In the quadratic formula, the expression under the radical b²-4ac is called the discriminant. The discriminant indicates the number of real solutions of the equation. The solutions of a quadratic equation is also called its roots. Roots are the input values for which the related function is zero.

• if ​b² - 4ac > 0, there are two real solutions

• if b² - 4ac < 0, there are no real solutions

• if b² - 4ac = 0, then there is one real solution.​

Understand How to Use the Discriminant to Find the Amount of Solutions

​https://youtu.be/XDiFIG-FvKk

Multiple Choice

Use the discriminant to find the number of roots of the equation?

$$x^2-10x+25\ =0$$  

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Multiple Choice

Use the discriminant to find the number of roots of the equation?

$$-x^2-6x+10=0$$  

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• 1

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​Lesson Summary

​Questions, Comments, Concerns?????