Unit Goal = What's the big idea?

I'm thinking that big ideas and goals are connected. If students don't take away the big idea from the unit, then I haven't achieved my goal(s). For my unit, we are learning about quadratic equations. The big ideas include being able to recognize a quadratic equation as being an equation that has a value that is squared (AKA to the power of 2). Other goals are that students understand that quadratics are nonlinear and that they have two solutions. We've been working on linear equations and exponential equations so far this year. I not only want students to be able to easily recognize each of these 3 types by just looking at the format, but also to know how they relate to the world around them, like projectile motion, such as this ski jumper.