4.8B Use the Quadratic Formula and the DiscriminantName: ______

Objective: To use the discriminant to determine the number of solutions.

Algebra 2 Standard 8.0

TheQuadratic Formula: , b2 – 4ac is called the discriminant

Examples: Solve using the Quadratic Formula:

Be sure the original equation is in standard form (ax2 + bx + c = 0) before you solve.

You will obtain two real solutions, one real solution, or two imaginary solutions.

1. Solve x2 = – 6x – 4

2. Solve 4x2 – 12x = –9

3. You Try: Solve 7x – 5x2 – 4 = 2x+3

Using the Discriminant of ax2 + bx + c = 0

Value of the discriminant / b2 – 4ac > 0 / b2 – 4ac = 0 / b2 – 4ac < 0
Number and type of solutions / ______real solutions / _____ real solution / Two ______solutions
Graph of
ax2 + bx + c = 0 /
______x-intercepts /
______x-intercept /

______x-intercepts

Example4: Find the discriminant of the quadratic equation and give the number and type of solutions of the equation.

a. x2 + 10x + 23 = 0b. x2 + 10x + 25 = 0c. x2 + 10x + 27 = 0

You Try: Find the discriminant of the quadratic equation and give the number and type of solutions of the equation.

a. 3x2 + 12x + 12 = 0b. 2x2 + 4x – 4 = 0c. 7x2– 2x= 5

Modeling Launched Objects:
Recall that the formula for a dropped object is h = –16t2 +h0. For an object that is launched or thrown, an extra term v0t must be added to the model to account for the object’s initial vertical (upward) velocityv0 (in feet per second). Recall that h is the height (in feet), t is the time in motion (in seconds), and h0 is the initial height (in feet).

h = –16t2 +h0 Object is dropped

h = –16t2+ v0t +h0 Object is launched or thrown

The value of v0can be ______, ______, or ______, depending on whether the object is launched upward, downward, or parallel to the ground.

Example5: A basketball player passes the ball to a teammate. The ball leaves the player’s hand 5 feet about the ground and has an initial vertical velocity of 55 feet per second. The teammate catches the ball when it returns to a height of 5 feet. How long was the ball in the air?

4.8B Notes