Write down the standard mathematical form of a quadratic equation as y = ax^2 + bx + c, where "a" is any real number except "0," "b" is any real number and "c" is any real number.
Create an equation for a quadratic graph. Use larger numbers for "a" if you want to create a steep parabola. Use a positive value of "a" if you want the parabola to open upwards. Use a negative value of "a" if you want the parabola to enter downward. Substitute the values a=1, b=0, and c=0 into the standard form given in Step 1 to obtain the equation y = 1*x^2 + 0*x + 0. Simplify this equation to obtain y = x^2, since zero multiplied by any number is 0 and zero added to any number is the number itself.
Use the online parabola graphing calculator given in the Resources section to graph the equation in Step 2 if you don't already have a favorite of your own. Type into the equation or function box of the online calculator the quadratic equation: y=x^2 or if your calculator requires, type in the numerical values of a, b, and c from step 2. Click the "graph," "plot" or "calculate" button on the online calculator. Observe that the parabola has its lowest point (vertex) at the point (0,0) on the x-axis, the parabola opens upward and the parabola is symmetrical about the y-axis of the graph.
Change the numerical value of the "c" term, 0, in Step 2, to 2, to shift the parabola up 2 units. Type into the function text box of the online calculator the function: y = x^2 + 2 or type 1 in the "a" textbox and 0 in the "b" textbox and 2 in the "c" textbox. Click the "graph," "plot" or "calculate" button on the online calculator. Observe that the parabola's lowest point (the vertex) is at the point (0,2) on the graph, the parabola opens upward, the parabola is symmetrical about the y-axis and the parabola is shifted 2 units above the x-axis.
Change the numerical value of the "c" term, 0, in step 2, from 2 to -3, to shift the parabola down 3 units below the x-axis. Type into the function text box of the online calculator the function: y = x^2 - 3 or type 1 in the "a" textbox and 0 in the "b" textbox and -3 in the "c" textbox. Click the "graph," "plot" or "calculate" button on the online calculator. Observe that the parabola's lowest point (the vertex) is at the point (0,-3), the parabola opens upward and the parabola is symmetrical about the y-axis.
Use a negative number for the "a" value in the equation of the parabola to graph a parabola that opens down. Type into the function text box of the online calculator the function: y = -x^2 or or type -1 in the "a" textbox and 0 in the "b" textbox and 0 in the "c" textbox. Click the "graph," "plot" or "calculate" button on the online calculator. Observe that the parabola has its "highest" point at the point (0,0), is symmetrical about the y-axis and opens downward as opposed to upward (as was the case for the quadratic graphs of the other examples).