Life is not measured by the number of breaths we take, but by the moments that take our breath away.

The Quadratic Formula
A quadratic equation written in standard form ax
2  bx
 
0 can be solved with the Quadratic Formula.
(Useful when factoring by
hand is not an option.)
Ex1) 3 x
2 
23 x
 
40 x

 b
2 a
 b
2
2
 a
4 ac
Ex2) 3 x
2   
4

Ex3) The longer leg of a right triangle is 1 unit longer than the shorter leg. The hypotenuse is 3 units long. What is the length of the shorter leg?
3
x + 1 x

Quadratic Equations can have real or complex (imaginary) solutions. You can determine the type and number of solutions by finding the discriminant.
x

 b
2 a
 b
2 
4 a c
2 a
The discriminant of a quadratic equation is b
2 
4 ac

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

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 = –16 t 2 + 25 t + 6. If the ball makes it to where the wall is, will it go over the wall or hit the wall?

HW: 4-19 first column AND #5, 31, 35, 37, 40
Life is not measured by the number of breaths we take, but by the moments that take our breath away.