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?