Question #5059c

F(x) is just a way to write “a function in x”, or, the other side is an expression that tells you how THIS (left) side changes (Functions) when you change the value used for ‘x’ in the expression.

When we had “fixed” mathematical equation problems we used x or y. At the earliest we just learned ‘results’, like 2 + 3 = 5. Once we understood that (our addition and multiplication tables) we made it more general by using a letter symbol (x or y for example) to show that it could vary if the numbers on the other side changed.

For example y = 2 + 3. y = 5, just like before. Then y = 4 + 3 is another expression, and y = 7. The answer is still simply from our “addition” tables, but we begin to see how the “answer” in the table is derived from the “expression” 4 + 3.

We make these progressive “generalizations” in order to be able to apply the math that we know works to situations that are harder to write down as a single number – or which may include many numbers.

The next “generalization” is when we make one of the terms in our simple expression a “variable”. It is the number that we can “vary” as in my previous example. Instead of y = 2 + 3 and y = 4 + 3 as separate equation expressions, we can see that the first term varied – and changed the result.

Using another letter to represent the variability we use ‘x’, and write y = x + 3. NOW we can change ‘x’ to any number we like and calculate the new ‘y’ value.

Finally, when we want to make a general mathematical description of how that ‘y’ changes when we change the value of ‘x’, we call it a “function of x”, and write it as F(x) instead of y.

SO, the equation you posted is “a function of x that satisfies (solves) the expression on the other side of the equals sign”. In this case it is a quadratic function that can be “solved” for its root(s) (where y = 0) or just the general list of values of the expression, which can also be plotted as a graph.