The road to success is always under construction!!

 To graph parabolas what do you think the single most important point is that you should know?  THE VERTEX  It gives you a home base to work off of.

 Once you identify your vertex, it is important that you plot at least four other points.  Where should these points be?  At least two should go on either side.

 To decide this, the easiest thing to do is use the step pattern.  What is the step pattern?  The step pattern is the pattern which tells you how much to go up or down for every one unit that you go over.  The step pattern is based off of the first differences in a quadratic.

 In the most basic quadratic y=x 2 the first differences are 1,3,5  IMPORTANT  This means that for any parabola with an “a” of 1 or -1, it will follow the 1,3,5 step pattern.  You should memorize this!!

Ex. Graph the following parabolas on the given grid a)y=x 2 b)Y=-x 2

 This is easy.  All we do is multiply the 1,3,5 step pattern by whatever the new “a” value is  For example if you have y=2x 2, the step pattern would be 2,6,10  For y = 0.5x 2, the step pattern would be 0.5,1.5,2.5  What would the step pattern be for y=3x 2

Graph the following on the grid provided Ex. 1.y=2x 2 2.Y=0.5x 2 3.Y=-2x 2

 So what if we get an equation with all of the transformations?  Ex y=2(x-3) 2 -4  Steps:  1. Find the vertex  2. Apply the step pattern

Graph: y=2(x-3) 2 -4

 Do you still use the step pattern?  Probably NOT.  In cases like this it is better to use a table of values.

 Graph f(x)=0.37(x+4) 2 -3  Step 1. Plot the vertex  Step 2. Choose two values to plug in for x and then to solve for y.

 I’ll choose to plug in -3 and -2 for x  F(-3)= This means when I go one to the right of the vertex, the y value is  By symmetry I also know that if I go one to the left of the vertex f(-5) =-2.63

 Now go two to the right of the vertex.  F(-2)= This means when I go two to the right of the vertex the y value is  By symmetry if I go two to the left of the vertex, f(-6)=-1.52

 For most parabolas you can simply use the step pattern and finish the graph very quickly  If the numbers involve long strings of decimals a table of values is probably more appropriate.