1. 4.8 – Use the Quadratic Formula and the Discriminant

2. 4.8 – Use the Quadratic Formula and the Discriminant
Example 1:
Solve x2 + 3x = 2

3. 4.8 – Use the Quadratic Formula and the Discriminant
Example 2:
Solve 25x2 - 18x= 12x – 9

4. 4.8 – Use the Quadratic Formula and the Discriminant
Example 3:
Solve -x2 + 4x = 5

5. 4.8 – Use the Quadratic Formula and the Discriminant
In the quadratic formula, the expression
b2 - 4ac is called the discriminant of the assosciated equation ax2 + bx + c = 0
You can use the discriminant of a quadratic equation to determine the equation’s number and type of solutions.

6. 4.8 – Use the Quadratic Formula and the Discriminant

7. 4.8 – Use the Quadratic Formula and the Discriminant
Example 4:
Find the discriminant of the quadratic equation and give the number and type of solutions of the equation.
x2 – 8x + 17 = 0
x2 – 8x + 16 = 0
x2 – 8x + 15 = 0

8. 4.8 – Use the Quadratic Formula and the Discriminant
For an object that is dropped: h = -16t2 + h0
For an object that is launched or thrown:
h = -16t2 +v0t+ h0
Initial velocity can be positive, negative, or zero depending on whether the object is launched upward, downward, or parallel to the ground.

9. 4.8 – Use the Quadratic Formula and the Discriminant
Example 5:
A juggler tosses a ball into the air. The ball leaves the juggler’s hand 4 feet above the ground and has an initial velocity of 40 feet per second. The juggler catches the ball when it falls back to a height of 3 feet. How long is the ball in the air?

10. 4.8 – Use the Quadratic Formula and the Discriminant
Example 6:
A basketball player passes a ball to a teammate. The ball leaves the player’s hand 5 feet above the ground and has an initial velocity of 55 feet per second. The teammate catches the ball when it returns to a height of 5 feet. How long is the ball in the air?