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47 lines
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Markdown
47 lines
2.0 KiB
Markdown
# Unit 3: Solving Equations and Inequailties
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## Equations
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- a ```mathematical statement``` in which the value on the ```left side``` equals the value on the ```right side``` of the equal sign
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- To ```solve``` and equation is to find the variable that makes the statement true
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### Methods to solve an equation
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1. Expand and simplify both sides
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2. Isolate using reverse order of operations
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3. Check the solution by plugging the variable back into the equation and check if the ```left side``` equals the ```right side```
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## Absolute Values
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- There are 2 cases. For this sort of equation, you must split the equation into 2 separate equations. One of the
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- equations will have the absolute bracket be positive while the other negative.
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- Absolute values are written in the form $`| x |`$
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- where
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$`
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| x | =
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\begin{cases}
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x, & \text{if } x > 0\\
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0, & \text{if } x = 0\\
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-x, & \text{if } x < 0
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\end{cases}
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`$
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## Quadractic Equations
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- ```Quadratic Function```: A parabolic graph where the axis of symmetry is parallel to the y-axis
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- ```Quadratic Equation```: This function is set equal to ```0```. The solution to the equation are called ```roots```
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- Solve quadratic equation by:
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1. Isolation
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- $`a(x+b)^2 + k = 0`$
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2. Factor using zero-product property
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- ```The Zero Factor Property``` refers to when $`a \times b=0`$, then either $`a=0`$ or $`b=0`$.
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- $`(x-a)(x-b)=0`$
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- $`x = a, b`$
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- <img src="http://www.assignmentpoint.com/wp-content/uploads/2017/12/Quadratic-Expression-1.jpg" width="400">
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**Note:**
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- $`\sqrt{x^2} = \plusmn x`$ (There are 2 possible solutions)
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- ```Distrubutive Property``` - This is opening the bracket. $`a(x+y) = ax+ay`$
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## Tips
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- ```Absolute Values``` can have 2 solutions
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- ```Quadratics``` can also have 2 solutions
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- Make sure to do the reverse when moving things to the other side, meaning a positive on the ```left side``` becomes a negative on the ```right side```
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