SOLUTION: What is the equation of the parabola: Vertex at (2,-3): focus at (2, -5)? I really don't understand where in the equation the focus and vertex would be placed. Thank you.

Question 72742This question is from textbook Algebra and Trigonometry
: What is the equation of the parabola: Vertex at (2,-3): focus at (2, -5)? I really don't understand where in the equation the focus and vertex would be placed. Thank you. This question is from textbook Algebra and Trigonometry

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
What is the equation of the parabola: Vertex at (2,-3): focus at (2, -5)? I really don't understand where in the equation the focus and vertex would be placed. Thank you.
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Plot the two points so you can see which way the parabola opens.
Vertex at (2,-3) and focus to the left at (2,-5) indicates it
opens to the left.
So the general form for the equation is (y-k)^2=4p(x-h)
Since the vertex is at (2,3) h=2 and k=3
Since the distance from the vertex to the focus is -3, 4p=-3 and p=-3/4
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So the equation is (y+3)^2=4(-3/4)(x-2)
-3(x-2)=(y+3)^2
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Cheers,
Stan H.

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