4.8 – Use the Quadratic Formula and the Discriminant

4.8 – Use the Quadratic Formula and the Discriminant

Example 1:

Solve x2 + 3x = 2

4.8 – Use the Quadratic Formula and the Discriminant

Example 2:

Solve 25x2 - 18x= 12x – 9

4.8 – Use the Quadratic Formula and the Discriminant

Example 3:

Solve -x2 + 4x = 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.

4.8 – Use the Quadratic Formula and the Discriminant

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.

a. x2 – 8x + 17 = 0

b. x2 – 8x + 16 = 0

c. x2 – 8x + 15 = 0

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.

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?

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?