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# 4.7 The Quadratic Formula

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### 4.7 The Quadratic Formula

1. 1. 4.7 THE QUADRATIC FORMULA
2. 2. SOLVING QUADRATIC EQUATIONS Remember: when we solve quadratic equations, we are finding the values of the zeros (also called the x – intercepts and the roots) So far, we have learned to solve quadratic equations by factoring, graphing, and completing the square
3. 3. THE QUADRATIC FORMULA The quadratic formula can be used to solve quadratic equations Given: The Quadratic Formula is
4. 4. USING THE QUADRATIC FORMULA1. Write the function in standard form2. Plug the values of a, b, and c into the quadratic formula3. Simplify
5. 5. EXAMPLE: SOLVE BY USING THE QUADRATICFORMULA
6. 6. EXAMPLE: SOLVE BY USING THE QUADRATICFORMULA
7. 7. EXAMPLE: APPLYING THE QUADRATICFORMULA Your school’s jazz band is selling CDs as a fundraiser. The total profit, p, depends on the amount, x, that your band charges for each CD. The equation models the profit of the fundraiser. What is the least amount, in dollars, you can charge for a CD to make a profit of \$200?
8. 8. THE DISCRIMINANT The discriminant of a quadratic equation tells you how many solutions a quadratic equation has.  The discriminant is the expression
9. 9. USING THE DISCRIMINANT1. Evaluate2. Interpret the discriminant (analyze using the chart)
10. 10. EXAMPLE: EVALUATE THE DISCRIMINANT FOR EACHEQUATION. DETERMINE THE NUMBER OF REALSOLUTIONS.
11. 11. EXAMPLE: EVALUATE THE DISCRIMINANT FOR EACHEQUATION. DETERMINE THE NUMBER OF REALSOLUTIONS.
12. 12. EXAMPLE: EVALUATE THE DISCRIMINANT FOR EACHEQUATION. DETERMINE THE NUMBER OF REALSOLUTIONS.
13. 13. EXAMPLE: USING THE DISCRIMINANT You hit a golf ball into the air from a height of 1 inch above the ground with an initial velocity of 85 ft/s. The function models the height in feet, of the ball at time t in seconds . Will the ball reach a height of 115 ft? (use the discriminant to determine how many, if any, solutions there are)
14. 14. HOMEWORK P 245 # 11 – 37 odd, 41 – 55 odd, 59 – 61 all, 68