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# Alg2 lesson 6-5

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### Alg2 lesson 6-5

1. 1. Quadratic Formula:<br />If ax2 + bx + c = 0, then<br />
2. 2. page 313<br />
3. 3. Solve by using the Quadratic Formula.<br />or<br />Two real solutions (both rational)<br />Example 5-1a<br />
4. 4. The x-intercept(s) of the graph of<br />f(x) = ax2 + bx + c <br />are also the solution(s) of the equation<br />ax2 + bx + c = 0 <br />
5. 5. Solve by using the Quadratic Formula.<br />or<br />Two real solutions (both rational)<br />Example 5-1a<br />
6. 6. Solve by using the Quadratic Formula.<br />or<br />Two real solutions (both rational)<br />Example 5-1a<br />
7. 7. Solve byusingtheQuadraticFormula.<br />=<br />One real solution<br />Example 5-2a<br />
8. 8. Solve by using the Quadratic Formula.<br />The two solutions are the complex<br />numbers and<br />Example 5-4a<br />
9. 9. In the quadratic formula, b2 – 4ac is called the discriminant<br />
10. 10. Find the value of the discriminant for . Then describe the number and type of roots for the equation.<br />Answer: The discriminant is 0, so there is one rational root.<br />Example 5-5a<br />
11. 11. Find the value of the discriminant for . Then describe the number and type of roots for the equation.<br />Answer: The discriminant is negative, so there are two complex roots.<br />Example 5-5a<br />
12. 12. Find the value of the discriminant for . Then describe the number and type of roots for the equation.<br />Answer: The discriminant is 80, which is not a perfect square. Therefore, there aretwo irrational roots.<br />Example 5-5a<br />
13. 13. Find the value of the discriminant for . Then describe the number and type of roots for the equation.<br />Answer: The discriminant is 81, which is a perfect square. Therefore, there are tworational roots.<br />Example 5-5a<br />