*I completely understand and here's where I am going to try to help!*

Do you see how the ball will reach 20 feet on the way up and on the way down? We will now be solving for t using the quadratic formula. Our actual times were pretty close to our estimates.

Just don't forget that when you solve a quadratic equation, you must have the equation set equal to 0.

Therefore, we had to subtract 20 from both sides in order to have the equation set to 0.

You've now seen it all when it comes to projectiles! Hopefully you've been able to understand how to solve problems involving quadratic equations.

I also hope that you better understand these common velocity equations and how to think about what this problem looks like graphically in order to help you to understand which process or formula to use in order to solve the problem.

When you throw a ball (or shoot an arrow, fire a missile or throw a stone) it goes up into the air, slowing as it travels, then comes down again faster and faster ... and a Quadratic Equation tells you its position at all times! There are many ways to solve it, here we will factor it using the "Find two numbers that multiply to give a×c, and add to give b" method in Factoring Quadratics: a×c = A very profitable venture.

Let's first take a minute to understand this problem and what it means. So, here's a mathematical picture that I see in my head. The equation that gives the height (h) of the ball at any time (t) is: h(t)= -16t Now, we've changed the question and we want to know how long did it take the ball to reach the ground. The problem didn't mention anything about a ground. I'm thinking that this may not be a factorable equation. The first time doesn't make sense because it's negative.

Let's take a look at the picture "in our mind" again. This is the calculation for when the ball was on the ground initially before it was shot.

Don't be surprised if many of your exercises work out as "neatly" as the above examples have.

Many textbooks still engineer their exercises carefully, so that you can solve by factoring (that is, by quickly doing the algebra).

## Comments How To Solve A Quadratic Word Problem