Solving Quadratic Equations Using the Quadratic Formula MA.912.A.7.2 Solve quadratic equations over the real numbers by factoring and by using the quadratic.

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Presentation transcript:

Solving Quadratic Equations Using the Quadratic Formula MA.912.A.7.2 Solve quadratic equations over the real numbers by factoring and by using the quadratic formula.

The Quadratic Formula The solutions of a quadratic equation written in Standard Form, ax 2 + bx + c = 0, can be found by Using the Quadratic Formula. Click on the link below to view a song to help you memorize it.

Deriving the Quadratic Formula by Completing the Square. Divide both sides by “a”. Subtract constant from both sides.

Deriving the Quadratic Formula by Completing the Square. Complete The Square Factor the Perfect Square Trinomial Simplify expression on the left side by finding the LCD

Deriving the Quadratic Formula by Completing the Square. Take the square root of both sides Solve absolute value/ Simplify radical

Deriving the Quadratic Formula by Completing the Square. Isolate x Simplify Congratulations! You have derived The Quadratic Formula

#1 Solve using the quadratic formula.

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#1 Solve by factoring

#2 Solve by factoring This quadratic is Prime (will not factor), The Quadratic Formula must be used!

#2 Solve using the quadratic formula. Exact Solution Approx Solution

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#3 Solve using the quadratic formula The is not a real number, therefore this equation has ‘ NO Real Solution ’

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#4 Solve using the quadratic formula Would factoring work to solve this equation?

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#5 Solve using the quadratic formula. Exact Solution Approx Solution

#5 What if we move everything to the right side? Exact Solution Approx Solution

Graph Clink on link for graphing calculator.

The Discriminant The expression inside the radical in the quadratic formula is called the Discriminant. The discriminant can be used to determine the number of solutions that a quadratic has.

Understanding the discriminant Discriminant # of real solutions 1 real rational solution No real solution Perfect square Not Perfect 2 real rational solutions 2 real irrational solutions

#6 Find the discriminant and describe the solutions to the equations. 2 Real Rational Solutions

#7 Find the discriminant and describe the solutions to the equations. No Real Solutions

#8 Find the discriminant and describe the solutions to the equations. 2 Real Irrational Solutions

#9 Find the discriminant and describe the solutions to the equations. 1 Real Rational Solution