Mathematics is a mind game that takes a lot of logical reasoning. It plays tricks on the mind and has a way of making simple things rather complex. But the moment you know and understand how things work, you will be able to solve the toughest problems in whatever category it might be.
Have you been having issues with solving vertex form of a quadratic equation? You won’t anymore with all you are about to learn here. We have been able to simplify the working process and break down all the complex logic that it involves.
General Overview Of The Formula
Solving the vertex form of a quadratic equation involves simple and straight forward steps with less logical reasoning. From our basic knowledge of quadratic functions, you should remember its basic rule which states a shift in the horizontal shifts towards the (y-axis) signifies an inward parenthesis movement while a vertical shift is considered an outside parenthesis.
Based on this rule, we will want to solve the vertex form of a quadratic equation by shifting 3 units right and 4 units downwards. In turn, this will modify our general quadratic function of y=x^2 to y=(x-3)^2-4. From this, we should be able to extract the coordinate of a vertex which is (3, -4)
Supposing our equation was given in a standard form, the process is quite similar. all that you need to do is to use completing the square method to get this vertex form. Let’s take, for example, we have a standard form equation y=x^2+6x+8 how can this be solved to a vertex form? Here, the first thing you need to do is to complete the square of the quadratic equation by adding (b/2)^2, here your b= 6.
After a quick calculation, you should come up with 9 as an answer. Then, you can complete the square by adding 9 and subtracting 9 simultaneously (y=x^2+6x+9+8-9). Lastly, factorize the equation to get something like y=(x+3)^2-1.
From this, you can easily extract your vertex form which is at (-3,-1).
How Can you master these basic steps of solving the vertex form of a quadratic equation
Just like every other mathematical problem, repetition is the key to perfection. To master it, you take a few more examples and try solving them using this method. By the time you repeat this countless times, it will soon become a part of you.
Moreso, you need to understand that solving vertex form of a quadratic equation is quite different from other mathematical problems with formulas. Here, you don’t need to memorize the formulas, all you just need to do is understand the whole process and you will find it quite easy to solve any kind of problems.