Quadratic equations are used to solve different kinds of problems in Math. You can use it to find the equation of a parabola and plot it on a graph. Every parabolic equation consists of a highest and the lowest point. It is commonly referred to as the vertex of the equation. Before you plot the equation, it is important to find the vertex formula. It is like an equation that you can derive from the quadratic equation itself. When you get that you can put the values to find the design of the graph.
Every parabolic equation has a point where it touches the axis of symmetry. To know about this you need to find out the coefficient of the square of the x point. If it is positive, the vertex will be located at the lowest point. That means that the graph will be more like a U-shape structure and the vertex will be at the bottom. In case the x square coefficient is negative, the scenario will change. The vertex will come at the top of the U-shape instead of the bottom.
Finding the vertex
There is a particular vertex form that you need to find from an equation. An example of this quadratic equation can be shown as y = A(x – h)2 + k. Here, you can see there are two variables, h, and k. These are the horizontal and vertical shifts of the parabola that you want to design. To make things simple you need to compare this with the equation which is provided in your question. Follow these steps to know how you can get the vertex:
- Step 1: Getting the values: You will have the quadratic equation in the form of ax2+bx+c=0. Here, you have to just put down the values of a, b and c. You will get this when you compare both the equations directly. Make sure that you do not ignore the signs of the values as well.
- Step 2: Putting the formulae: There is a generalized formula for the vertex of a parabola. Learn that and apply it to find the exact values in your problem. For example, if you want the x- part of the vertex, the formula is -b/2a. Once you substitute it you will get the value of x directly from this vertex formula.
- Step 3: Substituting x in the original equation: Once you find the value of x, the process becomes much simpler. You just have to substitute x in the quadratic equation that you already have. In question, you will have an equation y= ax2+bx+c. Put the value of x along with the rest of the values to find out your y part.
- Step 4: Write both x and y together: The vertex is the middle point of a parabola. To find, you need both the x and y coordinates in the graph. Now when you follow the above process, you will get both the coordinates. Put them side by side to get the answer that you need. When you find out the value(s), you can start putting the other points in the graph.
There are various other ways to find the vertex of a parabola as well. Beginners usually prefer this method as it is easy to apply. Plotting a graph requires a lot of shortcut formulas. It will help you to solve MCQs on time and get full marks. Cuemath is one such platform that provides online math classes and will help you grasp these equations and shortcuts. Here you get to know all the tricks and procedures to solve geometrical problems.