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y²-6x-24=0 (parabola)

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1 Answer

I may be wrong about this, but I'm going to assume the equation you'd like to solve is x2-6x-24=0, not the one you have listed above. (To solve for two variables, you generally need two equations or more.)
There are generally three ways to solve equations:
  1. numerically (using a table)
  2. graphically
  3. algebraically
  4. using the quadratic formula
To solve this quadratic equation numerically, you could make a table of values or simply guess and check x values for the related quadratic function y=x2-6x-24. For instance, when x=-2, y=(-2)2-6(-2)-24, so y=-10. This method may take awhile, because you'd have to keep plugging in x values until you find one that makes y=0.
To solve this equation graphically, you would take that table of values and graph them, or use a graphing calculator to graph the above quadratic function. You would then look for when the graph of the function intersects with the x-axis. These points (there will be two for a parabola) are called the functions zeros or roots and are the answer to the equation. Again, this may take awhile.
The best way to solve these is usually, however, is to use algebra. You can factor the equation to find the values that make the left side equal to zero. To factor these types of equations, you want to find two binomials that multiply to equal the expression on the left side of your equation. So you want to find a and b such that: