A quadratic function is one where the highest exponent of the independent variable is 2. The quadratic function can be written in the general form of, where a, b, and c are real numbers. However, the quadratic function can also be written in the standard form of , which is sometimes more preferred, where p and q are the x and y coordinates of the vertex, respectively.
The purpose of this task is to investigate the graph of a quadratic equation, the parabola, when the equation is written in the form. By analyzing p and q we can determine the vertex of the graph. Also, by increasing or decreasing the values of p or q, we can translate the parabola vertically and/or horizontally.
First, if we look at the functions y=x2 ,y=x2+3, y=x2-2 we know that all 3 are in general form. To convert general to standard form you will need to use the process called “completing the square” which goes as following: Ex.
Now if we convert the three functions mentioned above, in standard form respectively they are y=x020, y=x02+3 and y=x02-2. Now if we were to graph these points, either the standard or general form would work.
y=x2 , y=x020 y=x2+3 , y=x02+3
y=x2-2 , y=x02-2
Other examples of these types of graphs could be anything along the line of. An example of a parabola in the form of y=x2q with either a positive or negative q value could be y=x2+5 and y=x2-4. When we graph the two equations they are as...