What is the quadratic equation and what does it do?
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To give an ELI15:
Basic algebra equations are usually something like y = 2x + 4, which means that the variable y is two times x plus four.
So if y is how many pancakes you get from x number of eggs, then if you have 3 eggs, you’ll get 10 pancakes.
The question is, if you have a certain amount of pancakes, can we figure out how many eggs it took?
In this case what we do is the steps from before, but now backwards and opposite. The original was y is two times x plus four. The opposite of plus is minus, and times is divided. So backwards and opposite, it’s y minus four divided by two equals x.
As an equation: (y-4)/2 = x. So if we have 12 pancakes, we take away 4, we have 8 now. Then we divide 8 by 2, giving us 4. We used 4 eggs to get 12 pancakes.
Quadratic equations are ones that look like y = 4x^2 + 2x + 1. The quadratic formula is the same thing as the backwards and opposite step in basic algebra equations, except only when we have 0 as our y.
There are a bunch of equations where it’s important to find the x value for 0 = ax^2 + bx + c, which is why the quadratic formula finding zero is very common.
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