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Math IA (Quadratic Equations and Functions (Standard Form (Slope Formula…

- - - - x=-b/2a
    - - ax^2+bx+c
  - - - y=a(x-h)^2 +k
      - Vertex: (-h,k)
      - a.o.s: x=h
      - To find x, plug 0 for y and to find y, plug 0 for x
  - - - y=(ax+b)(x+d)
    - - then, plug x into the formula to get the y of the vertex
- - - - Make one of the variables the same same number as the other equation but with an opposite sign. Then, plug in your answer into either equation to get the other variable
    - - Rearrange the numbers in one equation to partially solve for the first variable. Then, plug you partially solved equation into the other answer and solve. Plug your found variable into either equation and solve
    - - Find at least 3 points from one equation and plot them on the graph. Once plotted, draw a linear line through each of the points then repeat with the other equation.
- - - - m is the slope
      - b = the y-intercept
    - - rise over run
      - y(1) - y(2)/ x(1) - x(2)
    - - Inconsistent
        
        Equations that have the same slope (m) value, but different y-intercepts (b). They appear as parallel lines as they don’t intersect to show a solution. This equation has no solution
      - Consistent Independent
        
        Equations that have different slopes. Their y-intercepts can be different or not. The lines intersect on a graph. The solution is the point of intersection.
      - Consistent Dependent
        
        Equations that have the same slope and the same y-intercept. The lines overlap on each other. Every point is an intersection, so it has an infinite number of solutions.