Essential Question What different methods can be used to solve
quadratic equations?
Slide 4
Quadratic Formula Quadratic Formula Graphically Click the
speaker to hear instructions
Slide 5
Solving Quadratics by Factoring Click the calculator to
continue
Slide 6
Solving Quadratics using the Quadratic Formula Click the
calculator to continue
Slide 7
Solving Quadratics Graphically Click the calculator to
continue
Slide 8
Solving Quadratics by Factoring x 2 - 9x + 20 = 0 Click for
additional help! (Stapel)
Slide 9
Solving Quadratics Graphically x 2 + 4x 20 = 2 Click for
additional help! (Tormoehlen, 2008)
Slide 10
2x 2 -10x 48 = 0 Solving Quadratics using the Quadratic Formula
Click for additional help! ("The quadratic formula," 2007)
Slide 11
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.
Slide 12
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
Sorry, your solution is incorrect.
Slide 13
Your solution is correct! x 2 - 9x + 20 = 0 (x 5)(x 4) = 0 x 5
= 0x 4 = 0 + 5 +5 + 4 +4 x = 5x = 4 Click here to continue
tutorialhere
Slide 14
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: x 2 12x + 15 = -8 +8 +8
x 2 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.
Slide 15
Click the star to try again 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: x 2 + 8x - 9 = 7 -8 -8 x 2
+ 8x - 17 = 0 Now that the equation is equal to zero, we would be
able to graph it and find its solutions. Sorry, your solution is
incorrect.
Slide 16
Your solution is correct! Click here to continue tutorialhere x
2 + 4x 20 = 2 -2 x 2 + 4x - 22 = 0 We now use our calculator to
graph the equation and find its solutions. x = -6x = 2
Slide 17
Here are some helpful hints! Click the pencil to try again 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: 1 x 2 - 4x - 3 = 0 a b c -4 to +4 Sorry,
your solution is incorrect.
Slide 18
Here are some helpful hints! Click the pencil to try again We
need to be careful when using our calculator to simplify the
quadratic formula. Example: In our calculator -4 2 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. Sorry, your solution is incorrect.
Slide 19
Click here to continue tutorialhere 2x 2 -10x 48 = 0 Your
solution is correct!
Slide 20
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 here to return to
home page.here Click to email Please first click here
Slide 21
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