Alg2: 2-4 to 2-8

​Alg2: 2-4 to 2-8

By: Isabella Jensen​

​Table of Contents

2-4 Compex Numbers: Slide 3

2-5 Completing the Square: Slide 4

2-6 The Quadratic Formula: Slide 5

2-7 Quadratic Inequalities: Slide 6

2-8 Systems Involving Quadratic Equations and Inequalities: Slide 7​

Subject | Subject

Some text here about the topic of discussion

Step #1: FOIL

Step #2: Combine alike terms

Step #3: replace i² to (-1)​² keeping the rest of the values the same

Step #4: solve then combine alike terms

Step #5: put in a + bi form resulting in 11-10i​

​Explanation

Put (3 + 2i)(1- 4i)​ in a + bi form.

​

KEY NOTES

• i = imaginary unit

• ( )( )= First Outer Inner L​ast (FOIL)

​Example

​2-4 Complex Numbers

​see link for written out process: https://www.google.com/search?q=complex+number+example+problem&sxsrf=ALiCzsaF3KL4GQLc3_Mo20s1ZYh0ElhNvg:1667337372031&source=lnms&tbm=isch&sa=X&ved=2ahUKEwjK_Z7e8437AhUkTjABHV03C4QQ_AUoAXoECAEQAw&biw=1440&bih=688&dpr=2#imgrc=hdjkSxZpP0RJvM

Step #1: set equation equal to zero

Step #2: ​simplify for smaller numbers

Step #3: move new "c" value on opposite side of "=" sign

Step #4: divide "b" into two equal alike values

Step #5: place value inside 2 pairs of parentheses (x-1)(x-1)

​Step #6: square the value inside double parentheses also placing it next to "c" with + or - sign to indicate addition or subtraction

Step #7: rewrite the double set of parentheses as only 1 set then square it (x-1)²

Step #8: add/subtract values on right of​ "=" sign

Step #9: square root both sides taking away the squared exponent

Step #10: make value on right side of "=" sign a +/- value

Step #11: add /subtract the left side value to the right setting the equation to x=

Step #12: add and subtract the left and right value​ to get two answers of 4 and -2

​Explanation

4x² - 8x = 32​

​

KEY NOTES

• ​must equal zero

• 2 answers

• reduce/ simplify if possible​

​Example

​2-5 Completing the Square

See link for written out process: https://www.google.com/search?q=completeing+the+square+example+problem&tbm=isch&ved=2ahUKEwibipDf8437AhVvQkIHHd40AMUQ2-cCegQIABAA&oq=completeing+the+square+example+problem&gs_lcp=CgNpbWcQAzoECCMQJzoHCAAQgAQQGDoECAAQQzoFCAAQgAQ6BggAEAcQHjoICAAQCBAHEB5Q7hdYhEtggkxoAHAAeACAAZUBiAGBDpIBBDIzLjKYAQCgAQGqAQtnd3Mtd2l6LWltZ8ABAQ&sclient=img&ei=nYxhY9vHNe-EieoP3umAqAw&bih=688&biw=1440#imgrc=M3uFBB9NKS2BHM

Step #1: ​identify your a, b, and c value

Step #2: plug values into formula including "+" and "-" signs​ to indicate whether the value is positive or negative

Step #3: solve and ensure ​everything is divided by 2a

Step #4: the result should be 2 "x" values​ of 5 and -3.

​Explanation

​2x² - 4x - 30 = 0

​

KEY NOTES

• must know a, b, and c value

• x=-b +/- √​b² - 4ac / 2a

• must be set equal to zero​

​Example

​2-6 The Quadratic Formula

See link for written out process https://www.google.com/search?q=using+quadratic+formula+example+problem&tbm=isch&ved=2ahUKEwis2JjD9I37AhVCLVMKHdVKBywQ2-cCegQIABAA&oq=using+quadratic+formula+example+problem&gs_lcp=CgNpbWcQAzoECAAQQzoFCAAQgAQ6BggAEAcQHjoICAAQCBAHEB46BggAEAgQHlCuEFjcOGCoO2gAcAB4AIABfogB6w6SAQQyNS4xmAEAoAEBqgELZ3dzLXdpei1pbWfAAQE&sclient=img&ei=b41hY-zkLMLazALVlZ3gAg&bih=688&biw=1440#imgrc=9Mw5nxMKAJjfwM

​Step #1: factor

Step #2: set factored values to zero

Step #3: Results should be 2 solutions of -5 and 4 with -5 being the only true solution as -5<​0

​

​Explanation

​x² + x - 20 < 0

​

KEY POINTS

• must be set to zero on one side usually the right

​Example

​2-7 Quadratic Inequalities

See link for written out process/video: https://www.google.com/search?q=graphing+quadratic+inequalities+example+problem&tbm=isch&ved=2ahUKEwiV77vQ2ZL7AhXi8lMKHbL3BFgQ2-cCegQIABAA&oq=graphing+quadratic+inequalities+example+problem&gs_lcp=CgNpbWcQAzIECCMQJzoHCAAQgAQQGFDAAljVLmC0MGgAcAB4AIABSogBlwaSAQIxMpgBAKABAaoBC2d3cy13aXotaW1nwAEB&sclient=img&ei=UhBkY5X-HuLlzwKy75PABQ&bih=688&biw=1440#imgrc=YhkjLhqX25uBOM

​Step #1: set both equations equal to each other

Step #2: move equation to one side of "=" sign to equal zero

Step #3: factor (can complete the square or do quadratic formula as well)

Step #4: set each new equation ​to "y="

Step #5: this results in 2 answers of 5 and -3​

​Explanation

​Find the following that represents all solutions to (x,y) to the system of equations shown

2y + 6 = x

y² - 9 = x

​

KEY POINTS

• set equal to each other then equal to zero

  ​

​Example

​2-8 Systems Involving Quadratic Equations and Inequalities

See link for written out process: https://www.google.com/search?q=Systems+Involving+Quadratic+Equations+and+Inequalities+example+problem&tbm=isch&ved=2ahUKEwjin5X_v5D7AhWtxikDHQyKCSAQ2-cCegQIABAA&oq=Systems+Involving+Quadratic+Equations+and+Inequalities+example+problem&gs_lcp=CgNpbWcQAzoECCMQJzoECAAQQzoFCAAQgARQpwhY3SxgqzBoAHAAeACAAVSIAeQCkgEBNZgBAKABAaoBC2d3cy13aXotaW1nwAEB&sclient=img&ei=AeliY6KbJ62Np8kPjJSmgAI&bih=688&biw=1440#imgrc=gG9tV3ghhs8S1M

Poll

END OF LESSON

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