Integrated Math III
Essential Question
What different methods can be used to
solve quadratic equations?
Click the speaker to hear instructions
Quadratic
Formula
Solving Quadratics
Graphically
Solving Quadratics by Factoring
Click the calculator to continue…
Solving Quadratics using the
Quadratic Formula
Click the calculator to continue…
Solving Quadratics Graphically
Click the calculator to continue…
Solving Quadratics by Factoring
2
x -
9x + 20 = 0
Click for additional help!
(Stapel)
Solving Quadratics Graphically
2
x + 4x – 20 = 2
Click for additional help!
(Tormoehlen, 2008)
Solving Quadratics using the
Quadratic Formula
2
2x -10x
– 48 = 0
Click for additional help!
("The quadratic formula," 2007)
Sorry, your solution is incorrect.
Here are some helpful hints!
 We must first identify our a, b, and c terms.
 To factor, we have to find the multiples of c that add up to b.
 It is important to remember that a negative times a
negative also gives you a positive.
Example: If c = 36, the multiples are
36 · 1
-36 · -1
18 · 2
-18 · -2
12 · 3
-12 · -3
6·6
-6 · - 6
Click the smiley face to try again…
Sorry, your solution is incorrect.
Here are some helpful hints!
 Once the equation is in factored form, we must remember
that it is still equal to zero.
 This means that we must set each one of our linear factors
equal to zero too.
 We then solve for x.
Example: (x + 7)(x – 2) = 0
x+7=0
-7 -7
x = -7
x-2=0
- 2 -2
x = -2
Click the smiley face to try again…
Your solution is correct!
Click here to continue tutorial
2
x - 9x + 20 = 0
(x – 5)(x – 4) = 0
x–5=0
+ 5 +5
x=5
x–4=0
+4
+4
x=4
Sorry, your solution is incorrect.
Here are some helpful hints!
 In order to solve quadratics, the equation must be equal to
zero.
 If not, we have to move all of the terms to one side of the
equation.
Example: x2 – 12x + 15 = -8
+8 +8
x2 – 12x + 23 = 0
Now that the equation is equal to zero, we would
be able to graph it and find its solutions.
Click the star to try again…
Sorry, your solution is incorrect.
Here are some helpful hints!
 In order to solve quadratics, the equation must be equal to
zero.
 If not, we have to move all of the terms to one side of the
equation.
 When you bring a positive number over an equals sign, you
must perform the opposite operation.
Example: x2 + 8x - 9 = 7
-8 -8
x2 + 8x - 17 = 0
Now that the equation is equal to zero, we would
be able to graph it and find its solutions.
Click the star to try again…
Your solution is correct!
Click here to continue tutorial
2
x +
4x – 20 = 2
-2 -2
x2 + 4x - 22 = 0
We now use our calculator to graph the equation and find its solutions.
x = -6
x=2
Sorry, your solution is incorrect.
Here are some helpful hints!
 We must first identify our a, b, and c terms.
 When plugging the terms into the quadratic formula, we
must remember that –b means to change the sign of b.
Example: 1x2 - 4x - 3 = 0
a
b
c
-4 to +4
 b  b2  4ac
x
2a
4  (4) 2  4(1)( 3)
x
2(1)
Click the pencil to try again…
Sorry, your solution is incorrect.
Here are some helpful hints!
 We
need to be careful when using our calculator to
simplify the quadratic formula.
Example:  4  (4)
2
2
In our calculator -42 is equal to -16. We know that this is not true. A
negative squared is always equal to a positive. To fix this mistake, we must
insert parenthesis around the negative number. The calculator will then
give us the correct solution.
4  (4) 2  4(1)( 3)
x
2(1)
Click the pencil to try again…
Your solution is correct!
Click here to continue tutorial
2
2x -10x – 48 = 0
10  (10)  4(2)( 48) 10  484 10  22
x


2(2)
4
4
10  22
10  22
x
x
4
4
x 8
x  3
Please first click here
Exit Ticket 3 – 2 – 1
Please email me the answers.
 Write 3 things you liked about this lesson.
 Write 2 things you learned.
 Write 1 question you have about solving quadratics.
Click to email
Click here to return to home page.
Resources
Stapel, E. (n.d.). Factoring quadratics: the simple case. Retrieved from
http://www.purplemath.com/modules/factquad.htm
The quadratic formula to solve quadratic equations. (2007). Retrieved from
http://www.mathwarehouse.com/quadratic/the-quadratic-formula.php
Tormoehlen, T. (Producer). (2008). Solving quadratic equations by graphing. [Web]. Retrieved
from http://www.youtube.com/watch?v=8Pk2VN6wzqU