1. THE QUADRATIC FORMULA §5.8

2. VIDEO TIME! Quadratic Forumlatic Quadratic Cups Song Quad Solve

3. THE QUADRATIC FORMULA A quadratic equation written in standard form ax 2 + bx + c = 0 can be solved with the Quadratic Formula.

4. EXAMPLE 1: USING THE QUADRATIC FORMULA Step 1) Write in standard form. Step 2) Find the values of a, b, and c. Step 3) Use the Quadratic Formula. Step 4) Simplify. The Quadratic Formula!

5. EXAMPLE 2: USING THE QUADRATIC FORMULA Step 1) Write in standard form. Step 2) Find the values of a, b, and c. Step 3) Use the Quadratic Formula. Step 4) Simplify. The Quadratic Formula!

6. EXAMPLE 3: USING THE QUADRATIC FORMULA Step 1) Write in standard form. Step 2) Find the values of a, b, and c. Step 3) Use the Quadratic Formula. Step 4) Simplify. The Quadratic Formula!

7. EXAMPLE 4: USING THE QUADRATIC FORMULA Step 1) Write in standard form. Step 2) Find the values of a, b, and c. Step 3) Use the Quadratic Formula. Step 4) Simplify. The Quadratic Formula! Now graph the related function,

8. USING THE DISCRIMINANT Quadratic equations can have real or complex solutions. You can determine the type and number of solutions by finding the discriminant. The discriminant of a quadratic equation in the form ax 2 + bx + c = 0 is the value of the expression b 2 – 4ac. Discriminant

9. USING THE DISCRIMINANT Value of the DiscriminantType and Number of Solutions for ax 2 + bx + c =0 Examples of Graphs of Related Functions y = ax 2 + bx + c b 2 – 4ac > 0 Two real solutionsTwo x-intercepts b 2 – 4ac = 0 One real solutionOne x-intercept b 2 – 4ac < 0 No real solutionsNo x-intercepts Is this possible? If so, what are the possible answers?

10. EXAMPLE 5: USING THE DISCRIMINANT Determine the type and number of solutions.

11. VOLLEYBALL Suppose a player makes a dig that propels the ball to the setter with an upward velocity of 25 ft/s. The function h = -16t 2 + 25t models the height h in feet of the ball at time t in seconds. Will the ball ever reach a height of 10 ft?

12. Step 1) Substitute 10 for h. Step 2) Find the values of a, b, and c. Step 3) Evaluate the discriminant. Will the ball ever reach a height of 8 feet?

13. Step 1) Substitute 8 for h. Step 2) Find the values of a, b, and c. Step 3) Evaluate the discriminant.

14. EXIT TICKETPICK 1 FROM EACH BOX TO SOLVE