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MATH 2201

MATH 2201. CHAPTER 7 - QUADRATIC EQUATIONS Section 7.3 The Quadratic Formula. Learning Goals for Section 7.3. Use the quadratic formula to determine the roots of a quadratic equation. Some tools that can help you: graphing calculator https ://www.desmos.com/calculator. Introduction.

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MATH 2201

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  1. MATH 2201 CHAPTER 7 - QUADRATIC EQUATIONS Section 7.3 The Quadratic Formula

  2. Learning Goals for Section 7.3 Use the quadratic formula to determine the roots of a quadratic equation.Some tools that can help you: • graphing calculator • https://www.desmos.com/calculator

  3. Introduction The quadratic formula determines the roots of a quadratic equation in the form ax² + bx + c = 0, where a ≠ 0.

  4. Solve the following equation: 6x² - 3 = 7x

  5. Solve the following equation: 12x² + 45 = 47x

  6. Solve: 2x² + 8x = 5 State your answer as an exact value.

  7. Solve: 5x² - 3 = 10x State your answer as an exact value.

  8. Homework • Page 419 #1, 2, 3, 4, 6

  9. Example A store rents an average of 750 video games each month at the current rate of $4.50. The owner of the store wants to raise the rental rate to increase the revenue to $6000 per month. However, for every $1 increase, they know that they will rent 30 fewer games each month. The following function relates the price increase, p, to the revenue, r: (4.5 + p)(750 – 30p) = r How many dollars will the owner have to increase the price by in order to reach this $6000 revenue?

  10. Example A landscaper is designing a rectangular garden, which will be 5.oo m wide by 6.25 m long. She has enough crushed rock to cover an area of 6.0 m² and wants to make a uniform border around the garden. How wide should the border be, if she wants to use all the crushed rock?

  11. Summary • The roots of a quadratic equation in the form ax² + bx + c = 0, where a ≠ 0, can be determined by using the quadratic formula:

  12. Summary • The quadratic formula can be used to solve any quadratic equation, even if the equation is not factorable • Sometimes the roots can be simplified to nice, neat answers • Sometimes we need to give the roots as an exact value because they can not be simplified

  13. Homework • Page 420 #5, 7, 8 a) c), 10

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