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The quadratic formula is used when you want to find the roots or zeros to a quadratic function such as:

f(x) = 2x² + 5x - 3

or, in the general form:

f(x) = ax² + bx + c
The quadratic formula will tell us for what x values f(x) equals zero.

Here is the formula:

Quadratic Formula

In our example, a = 2, b = 5, and c = -3 so by plugging those numbers into the above formula, we get x = 2/4 and x = -3.

You can plug those two x values back into the original equation and you’ll see that f(x) = 0.  This means the graph of the function crosses the x-axis at those points.

Now, a trickier type of problem involving the quadratic formula is when you are asked how many solutions a function has given its discriminant.  The discriminant is the portion of the function beneath the radical,

b² - 4ac

There are 3 possibilities:

1. Discriminant is positive - In this case, there are 2 solutions.
2. Discriminant is negative - In this case, there are 0 solutions.
3. Discriminant is zero - In this case, there is 1 solution.

Take a look at the quadratic formula and see if you can figure out why this is true!