Earlier years of education have taught us addition, subtraction, multiplication, division, fractions and decimals. We know how to square numbers and also find their square root. The first two years of high school require students to combine all they have learned about math thus far and discover how math can be used to solve complex, real world problems. The first two styles mathematics you will likely encounter are algebra and geometry. In order to gain a foothold in both of these, you will need to learn how to use the quadratic equation.

A boy standing on top of a seven-story building tosses a ball to his friend on the ground. The building is 21.34 meters tall and he throws the ball in a straight line at 30.85 meters per second. When will it reach the friend? These types of math problems can be written out as the quadratic equation. The standard form of the quadratic equation looks like this:

ax2 + bx + c = 0

This equation is not the solution to the problem. To find x, we must replace a, b and c and then restructure the equation into what is known as the quadratic formula.

After we have determine a, b and c we would attempt to solve the quadratic equation. In order to do so, we must use the quadratic formula, which is much different. It looks like this:

It should be noted that this equation assumes that a does not equal 0. In the above example with the boy on the rooftop, we would replace a, b and c with numbers that we are given. B would be 30.85 and C would be 21.34 while A would be a constant value relating to the force of gravity (not uncommonly 4.9 when dealing with meters).

Geometry
If you drew a diagram of the boy on the rooftop example, you may notice that the building, the path of the ball and the ground form a triangle. This shows us that the quadratic formula is also useful for solving geometric problems. Of course, if we’re looking for the length of one side of the triangle, you can just use the Pythagorean Theorem you have been practicing for some time now. The quadratic formula is used for more complex geometry such as shapes within shapes.