Quadratic Equations

Quadratic Equations. Carried Out By: Gonato, Frances Jayne October 27, 2022 Math Tutorial Performance Task.

Agenda. 10/27/2022. 2. 02 Examples of quadratic equations.

Agenda. 10/27/2022. 3. 02 Examples of quadratic equations.

01. Introduction. Quadratic equations is any equation that can be rearranged in standard form as where x represents an unknown, and a, b, and c represent known numbers, where a ≠ 0. There are multiple ways to solve a quadratic equation. I will tell you what they are and how to use them shortly..

01. Introduction. Quadratic equations is any equation that can be rearranged in standard form as where x represents an unknown, and a, b, and c represent known numbers, where a ≠ 0. There are multiple ways to solve a quadratic equation. I will tell you what they are and how to use them shortly..

02. Examples of quadratic equations.

Examples of quadratic equations. 10/27/2022. 7. Factoring (2x^2 – 6x = 4x).

10/27/2022. 8. Examples of quadratic equations. Factoring (2x^2 – 6x = 4x).

Factoring. For factoring we will be using “2x^2 – 6x = 4x” as an example 1st step is to transpose 4x (remember to always change the sign), after transposing 4x our equation should look like this “2x^2 – 6x – 4x = 0”. 2nd step is to add the like terms in our equation (like terms are the terms that contain the same variable which is raised to the same power) “2x^2 – 10x = 0”. After that the 3rd step is to get the common monomial factor or the cmf of 2x^2 – 10x = 0 which is equivalent to 2x so 2x^2 divided by 2x the answer is x – 10x divided by 2x the answer is 5 = 0 then we can get the factor as 2x = 0 and x – 5 = 0 therefore the value of x is x = 0 and x = 5.

Extracting Square Root. For extracting square root, we will be using “x^2 – 16 = 0” This one is simple because the 1st step is to transpose -16 (don’t forget to change the sign). After that the 2nd step is so get the square root of both “x^2” and “16”, the square root of “x^2” is x and the square root of “16” is +-4. Therefore, our final answer is “x = +-4”.

Quadratic Formula. For quadratic formula we will be using “x^2 – 3x + 2 = 0” Formula: 1st step is to figure out what A, B, and C is equivalent to, for our example “A is = to 1, B is = to -3, C is = to 2. 2nd step is to follow the formula and according to the formula our equation should look like this “x= -(-3) +- √(-3)^2 – 4 (1)(2)/2(1). 3rd step is to solve the equation and after doing that our solution should look like this “x = 3 +-√-9 – 8/2 = x = 3 +- 1/2. Since 1 is already a perfect square we will no longer need to get the square root of 1. 4th step is to solve “3 + 1/2 and 3 – 1/2” so x = 3 + 1/2 = 4/2 or 2 and x = 3 – 1/2 = 2/2 = 1. Therefore, the value of x is 2 and 1.

03. 10/27/2022. 12. Solution and Tutorial. Quadratic Formula.

Completing the square. For completing the square, we will be using “x^2 + 2x - 8 = 0" as an example the formula for completing the square is "ax^2 + bx + (b/2)^2 = c + (b/2)^2" and by following this formula you can solve the equation. 1 st step is to subtract 8 from both sides or we could simply transpose 8 (remember that when you transpose a term you must change the sign from – to + or + to -) and it becomes x^2 + 2x = 8. See how there’s a missing number between 2x and = 8? To get that missing number we move forward to the 2 nd step, “(b/2)^2 (in other words get the half of b and square it)” is our second step. By doing this we will get “(2/2)^2 = (1)^2 = 1” as our answer. The value of the missing number is 1 (remember to add the missing number to both sides). Our solution is now “x^2 + 2x + 1 = 8 + 1”. 3 rd step is to factor the equation. “(x + 1)^2 = 9” By doing this our equation is now factored, after that we get the square root of “(x + 1) and 9”. The square root of (x + 1)^2 is “x + 1”. The square root of 9 is “+-3”, our equation should look like this “x + 1 = +-3”. 4 th step is to transpose 1 and get the value of x “x = -1 +-3”. Last step is to solve “-1 + 3” and “-1 – 3”, -1 + 3 = 2 , “-1 – 3 = -4” ..

05. Closing. 10/27/2022. 14. How to Say Goodbye The New York Times.

05. Closing. 10/27/2022. 15. I hope this helped you understand how to solve quadratic equations. Thank you and have a wonderful day! <3.