There are three main ways to solve quadratic equations: factoring, using the quadratic formula, and completing the square. Not all quadratic equations can be solved using the factoring method, and depending on the equation, completing the square can be a bit confusing. This is where using the quadratic formula comes in handy. Although the quadratic formula can look intimidating, it is just a combination of substitution and basic math skills of multiplication, subtraction and square root (thank goodness for calculators!). I really like the graphic used in my video above that shows the substitution placeholders between the quadratic equation and the quadratic formula, helping to make the substitution straightforward and easy to visualize. Here is a link to the graphic. The video below is an introduction to the quadratic formula and shows how to use our prior knowledge of quadratic equations to solve them using the quadratic formula.
Khan Academy is an excellent resource for mathematics teachers, students, and parents. I especially like to use their videos as supplements to classroom instruction. As long as students can access the internet, they can view the videos to receive additional guidance from their phone or computer. I try always to post a link to a Khan Academy video that compliments my lesson plan, such as the one below for solving quadratic equations using the quadratic formula. This way, if a student did not understand my instruction, missed class due to illness or an extra-curricular activity, etc., they can watch the video to receive assistance. My favorite benefit of video instruction is that if there is one particular step that is causing a student frustration, they can pause the video, back up and re-watch just the portion that they need to review. If the student still is struggling after reviewing the video, they can ask specific questions in class or during my office hours to clarify.
Although I do not spend class time showing the proof of the quadratic formula, it is essential for students to understand how and why using the quadratic formula to solve quadratic equations actually works. I have attached the above be from Khan Academy which does a great job of explaining. If a written version is more your style to be able to see the individual steps a bit more clearly, here is a printed version from openstudy.com that shows each step of the quadratic formula proof. Both forms of media are excellent resources for students.