How do you find out the equation of a parabola given the vertex (1 1/2, 3), and it cuts the y axis at 7 1/2?

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Answer 1 · 2015-04-30T15:22:08

In this way:

The equation of the parabolae (#oo#) given the vertex are:

#y-y_v=a(x-x_v)^2#.

So:

#y-3=a(x-11/2)^2#.

If our parabola cuts the y-axis at #7 1/2=15/2#, it means that passes from the point #(15/2,0)#.

Let's use this condition to find #a#:

#0-3=a(15/2-11/2)^2rArr-3=a(4/2)^2rArr-3=4arArr#

#a=-3/4#.

So:

#y-3=-3/4(x-11/2)^2#.

And now, if you need, you can do the counts.