Nox: x=-4y^2-4y+1 Graph the following horizontal parabola. How would one get this answer. Please show work.
It is just about the same as a vertical parabola.
Use the quadratic formula to get the roots. These will go on the y axis because you are solving for x=0 (and the equation of the y axis IS x=0)
I got y= -1/2 + root2/2 and y= -1/2 - root2/2 So you can plot thes points
now the axis of symetry is y= -1/2 ( you should be able to see that from the value of the roots)
Substitute y= -1/2 inot the initial equation to get the x value of the turning point. I got x=2
So the turning point is (2, -0.5)
3 points is all you need to define a parabola so now you have finished.
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Now there are some interesting facts that it would be good for you to think about.
y = -4x
2 - 4x + 1 and x = -4y
2 + 4y +1 are called inverse functions. That is, they are each the inverse of the other one.
This is true for ANY equations where the x and the y swap places.
All inverse functions are reflections of each other about the line y=x.
Why don't you sketch the other functions and convince yourself that this is correct.
Or you could look at 2 really easy ones like y=2x and x=2y
anyway this can sometimes be a very handy thing to know when you are sketching, or dealing with functions.
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