Chapter 2.6 - The Quadratic Formula
Obj: SWBAT - Solve Equations Using the Quadratic Formula (Day 1)
The Quadratic Formula
If 𝑎𝑥 2 + 𝑏𝑥 + 𝑐 = 0, then the roots are found by using
𝑥=
−𝑏±√𝑏2 −4𝑎𝑐
2𝑎
Example 1: Find the zeros of this function
𝑓(𝑥 ) = 𝑥2 + 10𝑥 + 2
0 = 𝑥2 + 10𝑥 + 2
set equal to zero….can it be factored?
Find a, b, and c from the equation
and put into the Quadratic Formula
𝑥=
−𝑏±√𝑏2 −4𝑎𝑐
a=
2𝑎
b=
c=
Example 2: Solving Equation with Complex Zeros
2
a=
𝑓(𝑥 ) = 2𝑥 − 𝑥 + 2
Set equal to zero and use: 𝑥 =
−𝑏±√𝑏2 −4𝑎𝑐
b=
2𝑎
c=
You try: Find the zero’s of each function by using the quadratic formula
f(x)=3x2 -10x + 3
What quadratic function has a zero of 3 + i
Find the values of c that make the equation have one real solution
x2 + 8x + c
x2 + 2cx + 49 = 0
HW: p. 105-106 # 19,20,24,37,44*,57,60
44.
HW: p. 105-106 # 19,20,24,37,44*,57,60
Name _______________________________________ Per _____
Ch 2-9 Quadratic Formula Homework (Day 1) p.105/ 1-14 All
If 𝑎𝑥 2 + 𝑏𝑥 + 𝑐 = 0, then the roots are found by using
𝑥=
−𝑏±√𝑏 2 −4𝑎𝑐
2𝑎
1) THINK: How many roots, and what kind of roots do you get if:
𝑏2 − 4𝑎𝑐 > 0
𝑏2 − 4𝑎𝑐 = 0
𝑏2 − 4𝑎𝑐 < 0
(𝑏 2 − 4𝑎𝑐 𝑖𝑠 𝑐𝑎𝑙𝑙𝑒𝑑 𝑡ℎ𝑒 Discriminant − 𝑡ℎ𝑖𝑠 𝑖𝑠 𝑎 𝑝𝑟𝑒𝑣𝑖𝑒𝑤 𝑜𝑓 𝑡𝑜𝑚𝑜𝑟𝑟𝑜𝑤 ′ 𝑠 𝑙𝑒𝑠𝑠𝑜𝑛)
Find the zeros of each function using the method of your choice
(Factoring, Completing the Square, or the Quadratic Formula)
[Note: The Quadratic Formula is just another tool used to solve quadratic equations. It is NOT always
the best or most efficient method]
14) An athlete on a track team throws a shot put. The height y of the shot put in feet t
seconds is modeled by 𝑦 = −16𝑡 2 + 24.6𝑡 + 6.5. The horizontal distance x feet between
the athlete and the shot put is modeled by 𝑥 = 29.3𝑡. To the nearest foot, how far does
the shot put land from the athlete?
Let’s do number 2 together…what is the best method?