*reciprocal*function of a quadratic function. With a linear function we took, for instance, y= x-7 and flipped it to be y= 1/ (x-7). The same goes for y= 2x+27 which in turn would be 1/(2x+27).

- Let’s first start with the zeros, or x-intercepts, of our function 1/x^2-4, which are -2 and 2. In these cases, the y-value of this coordinate is 0. When we apply this to the reciprocal, the denominator becomes 0, making the fraction 1/0, which doesn’t really work. So, two vertical asymptotes are created, in which the graph comes near however does not touch the x-values of 2 and -2.Next is the y-intercept, in which the x value is always 0 and for the quadratic function, the y-intercept is -4 while the reciprocal is, of course, -1/4.

- Next are positive and negative intervals, which seem to follow the same trend for both linear and quadratic reciprocals. Why? Because if an x-value is positive, the reciprocal will of course be positive because the sign of the value is not changing. 2 will be 1/2 and -2 will be -1/2.

- Lastly we’ll briefly review increasing and decreasing intervals. Simply put, as the x-values for the quadratic function increase, the reciprocals for these values decrease.

1----->1

2-----> 1/2

3-----> 1/3

As the graph of the quadratic moves UP the reciprocal function moves DOWN. As the quadratic function INCREASES our reciprocal DECREASES.

1/2-----> 2

1/3-----> 3

As you can see, the same goes for fractions and negative x-values of our quadratic function and the x-values of the reciprocal quadratic function. As the x-values of the quadratic function DECREASE, the values of the reciprocal function INCREASE.

****For Ms. Burchat’s period 3/4 class:****

If you still don’t see the importance of conceptual understanding, recall her university horror story and be scared into caring about conceptual understanding! And another lifelong rule? Don’t let anyone call you slave.... Or **esclave**, servus, or **esclavo**. Or even * sklave *or abed for that matter.

Don’t ask me how I found it. =)

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