The Quadratic Formula
Sep 14th, 2008 by Dave
Many algebra students have a hard time remembering what the quadratic formula is and how to use it so here is a refresher.
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:
- Discriminant is positive - In this case, there are 2 solutions.
- Discriminant is negative - In this case, there are 0 solutions.
- 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!
