Could someone show how to find the axis of symmetry, the focus, and the directrix of these parabolas. Thank you.
1.y^2=12x
2. y=4(x-2)^2
3. (x+2)^2=y-3
4. y= x^2+4x+1
Hi there, the axis of symmetry can be found by transforming a parabola into turning point form. When you know the turning point i.e (a,b) then axis of symmetry is simply x=a.
Your first equation is not a parabola. Equations 2 & 3 are pretty much in turning point form, equation 4 can be put into turning point form by completing the square.
http://en.wikipedia.org/wiki/Parabola
1. You have to consider two different types of paraboae:
a) vertical axis of symmetry. The general equation of such a parabola is
where V(k, h) is the vertex of the parabola and p is the distance between vertex V and focus F. The axis of symmetry has the equation x = k.
to #2.:
Therefore: ; ; axis of symmetry x = 2
b) horizontal axis of symmetry. The general equation of such a parabola is
where V(k, h) is the vertex of the parabola and p is the distance between vertex V and focus F. The axis of symmetry has the equation y = h.
to #1.:
Therefore: ; ; axis of symmetry: y = 0
The remaining examples have to be done in just the same way.
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Once you have learned the basic terms and techniques, please attempt at least one of the other exercises. If you get stuck, you will then be able to reply with a clear listing of your steps and reasoning so far, so we can "see" where you're having trouble, and then provide intelligent assistance.
Thank you!