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QUADRATIC EQUATIONS

QUADRATIC EQUATIONS. MSJC ~ San Jacinto Campus Math Center Workshop Series Theresa Hert. Simplify Radicals. Radicals with index 2 are referred to as square roots. Simplify Radicals. Break down the radicand, the number inside the radical, into prime factors.

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QUADRATIC EQUATIONS

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  1. QUADRATIC EQUATIONS MSJC ~ San Jacinto Campus Math Center Workshop Series Theresa Hert

  2. Simplify Radicals Radicals with index 2 are referred to as square roots.

  3. Simplify Radicals Break down the radicand, the number inside the radical, into prime factors. Circle a pair of matching factors, take out THE factor. Since no operation sign is visible, the “glue” holding everything together is Multiplication. When you bring a factor out of the radical, it gets multiplied to the number in front of the radical.

  4. Simplify the Radical

  5. Simplify Rational Expressions containing Radicals First simplify the radical. To reduce the fraction, Factor. Beware of addition. Plus sign – use one set of parentheses to factor out what is common.

  6. Simplify this Rational Expression containing a Radical

  7. Quadratic Equations contain both an equal sign and a variable with exponent 2. General form: ax2 + bx + c = 0

  8. A quadratic equation is an equation equivalent to an equation of the type ax2 + bx + c = 0, where a is nonzero • We can solve a quadratic equation by using the Quadratic Formula

  9. The Quadratic Formula • Solve the equation ax2 + bx + c = 0 for x by Completing the Square

  10. The Quadratic Formula The solution to the equation ax2 + bx + c = 0 is found by the Quadratic Formula:

  11. Solve this Quadratic Equationby using the Quadratic Formula 6y2 – 3y – 5 = 0 a = 6 b = -3 c = -5

  12. 6y2 – 3y – 5 = 0 a = 6 b = -3 c = -5 because of the addition, you can NOT reduce the fraction

  13. Ex: Use the Quadratic Formula to solve x2 + 7x + 6 = 0 1 7 6 Recall: For quadratic equation ax2 + bx + c = 0, the solutions to a quadratic equation are given by Identify a, b, and c in ax2 + bx + c = 0: a = b = c = 1 7 6 Now evaluate the quadratic formula at the identified values of a, b, and c

  14. x2 + 7x + 6 = 0 a = 1 b = 7 c = 6 x = ( - 7 + 5)/2 = - 1 and x = (-7 – 5)/2 = - 6 x = { - 1, - 6 }

  15. Ex: Use the Quadratic Formula to solve 2m2 + m – 10 = 0 1 2 – 10 Recall: For quadratic equation ax2 + bx + c = 0, the solutions to a quadratic equation are given by Identify a, b, and c in am2 + bm + c = 0: a = b = c = 2 1 - 10 Now evaluate the quadratic formula at the identified values of a, b, and c

  16. 2x2 + 1x – 10 = 0 a = 2 b = 1 c = -10 m = ( - 1 + 9)/4 = 2 and m = (-1 – 9)/4 = - 5/2 m = { 2, - 5/2 }

  17. Ex: Use the Quadratic Formula to solve x2 + 5x = -3 x2 + 5x + 3 = 0 1 3 + 5 Identify a, b, and c in ax2 + bx + c = 0: a = b = c = 1 + 5 3 Now evaluate the quadratic formula at the identified values of a, b, and c

  18. x2 + 5x + 3 = 0 a = 1 b = 5 c = 3

  19. Ex: Use the Quadratic Formula to solve 10x2 – 5x = 0 10x2 – 5x + 0 = 0 10 - 5 0 Identify a, b, and c in ax2 + bx + c = 0: a = b = c = 10 - 5 0 Now evaluate the quadratic formula at the identified values of a, b, and c

  20. 10x2 – 5x + 0 = 0 a = 10 b = -5 c = 0

  21. Solve:use the Quadratic Formula.

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