Graphing Parabolas
The graphs of quadratic equations (y = ax 2 + bx + c) are called parabolas. Sometimes the quadratic equation takes on the form of x = ay 2 + by + c.
There is a problem entering this equation in the calculator graphing list for two reasons:
a)it is not a function, and only functions can be entered in the Y= list locations,
b)the functions entered in the Y= list must be in terms of x, not y.
There are, however, two methods you can use to draw the graph of a parabola.
Method 1: Consider the "top" and "bottom" halves of the parabola as two different parts of the graph because each individually is a function. Solve the equation of the parabola for y and enter the two parts (that individually are functions) in two locations of the Y= list.
Method 2: Choose the parametric graphing mode of the calculator and enter the parametric equations of the parabola. It is not necessary to algebraically solve the equation for y. Parametric representations are equation pairs x = F(t), y = F(t) that have x and y each expressed in terms of a third parameter, t.
Example
Graph a parabola using two methods.
1. Graph the parabola x = y 2
2. Graph the parabola x = y 2
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1-3 View the graph.
GRAPH
x= y 2 -2
x+ 2 = y 2
y= +√ x + 2
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The graph of the equation y =
√x+ 2 is the "top half" of the parabola and the graph of the equation y = - √ x + 2 gives the "bottom half."
