5.8 The Quadratic Formula
Life is not measured by the number of breaths we
take, but by the moments that take our breath away.
Review – Warm Up
Solve by Factoring:
Solve by Completing the Square:
The Quadratic Formula
A quadratic equation written in standard form ax 2  bx  c  0 can be
solved with the Quadratic Formula.
(Useful when factoring by
hand is not an option.)
Ex1) 3x 2  23x  40
b
b  4ac
x

2a
2a
2
Ex2) 3x 2  2 x  4
Discriminant
Quadratic Equations can have real or complex (imaginary) solutions. You
can determine the type and number of solutions by finding the
discriminant.
b
b  4ac
x

2a
2a
2
The discriminant of a
quadratic equation is
b  4ac
2
Determine the type and number of solutions of by using the discriminant.
Ex4) x 2  6 x  8  0
Ex5) x 2  6 x  9  0
Ex6) x 2  6 x  10  0
Application
Ex7) A player throws a ball up and toward a wall that is 17 ft high. The
height h in feet of the ball t seconds after it leaves the player’s hand is
modeled by h = –16t 2 + 25t + 6. If the ball makes it to where the wall is,
will it go over the wall or hit the wall?
5.8 The Quadratic Formula
Homework (EXTRA CREDIT):
Pg 293 #4-19 first column AND #5, 31, 35, 37
CH 1, 2, 3, 5 test corrections due on FRIDAY!
FINAL EXAM FRIDAY